Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras

Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras

Author: Shari A. Prevost

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 113

ISBN-13: 0821825275

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We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.


Book Synopsis Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras by : Shari A. Prevost

Download or read book Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras written by Shari A. Prevost and published by American Mathematical Soc.. This book was released on 1992 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a new proof of the identities needed to exhibit an explicit [bold]Z-basis for the universal enveloping algebra associated to an affine Lie algebra. We then use the explicit [bold]Z-bases to extend Borcherds' description, via vertex operator representations, of a [bold]Z-form of the enveloping algebras for the simply-laced affine Lie algebras to the enveloping algebras associated to the unequal root length affine Lie algebras.

Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras

Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras

Author: David Mitzman

Publisher: American Mathematical Soc.

Published: 1985

Total Pages: 170

ISBN-13: 0821850431

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A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.


Book Synopsis Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras by : David Mitzman

Download or read book Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras written by David Mitzman and published by American Mathematical Soc.. This book was released on 1985 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.

Projective Modules over Lie Algebras of Cartan Type

Projective Modules over Lie Algebras of Cartan Type

Author: Daniel Ken Nakano

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 97

ISBN-13: 0821825305

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This paper investigates the question of linkage and block theory for Lie algebras of Cartan type. The second part of the paper deals mainly with block structure and projective modules of Lies algebras of types W and K.


Book Synopsis Projective Modules over Lie Algebras of Cartan Type by : Daniel Ken Nakano

Download or read book Projective Modules over Lie Algebras of Cartan Type written by Daniel Ken Nakano and published by American Mathematical Soc.. This book was released on 1992 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the question of linkage and block theory for Lie algebras of Cartan type. The second part of the paper deals mainly with block structure and projective modules of Lies algebras of types W and K.

Generalized Vertex Algebras and Relative Vertex Operators

Generalized Vertex Algebras and Relative Vertex Operators

Author: Chongying Dong

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 207

ISBN-13: 1461203538

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The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.


Book Synopsis Generalized Vertex Algebras and Relative Vertex Operators by : Chongying Dong

Download or read book Generalized Vertex Algebras and Relative Vertex Operators written by Chongying Dong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.

Invariant Subsemigroups of Lie Groups

Invariant Subsemigroups of Lie Groups

Author: Karl-Hermann Neeb

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 209

ISBN-13: 0821825623

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First we investigate the structure of Lie algebras with invariant cones and give a characterization of those Lie algebras containing pointed and generating invariant cones. Then we study the global structure of invariant Lie semigroups, and how far Lie's third theorem remains true for invariant cones and Lie semigroups.


Book Synopsis Invariant Subsemigroups of Lie Groups by : Karl-Hermann Neeb

Download or read book Invariant Subsemigroups of Lie Groups written by Karl-Hermann Neeb and published by American Mathematical Soc.. This book was released on 1993 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: First we investigate the structure of Lie algebras with invariant cones and give a characterization of those Lie algebras containing pointed and generating invariant cones. Then we study the global structure of invariant Lie semigroups, and how far Lie's third theorem remains true for invariant cones and Lie semigroups.

On Axiomatic Approaches to Vertex Operator Algebras and Modules

On Axiomatic Approaches to Vertex Operator Algebras and Modules

Author: Igor Frenkel

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 79

ISBN-13: 0821825550

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The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.


Book Synopsis On Axiomatic Approaches to Vertex Operator Algebras and Modules by : Igor Frenkel

Download or read book On Axiomatic Approaches to Vertex Operator Algebras and Modules written by Igor Frenkel and published by American Mathematical Soc.. This book was released on 1993 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic definitions and properties of vertex operator algebras, modules, intertwining operators and related concepts are presented, following a fundamental analogy with Lie algebra theory. The first steps in the development of the general theory are taken, and various natural and useful reformulations of the axioms are given. In particular, tensor products of algebras and modules, adjoint vertex operators and contragradient modules, adjoint intertwining operators and fusion rules are studied in greater depth. This paper lays the monodromy-free axiomatic foundation of the general theory of vertex operator algebras, modules and intertwining operators.

The Subregular Germ of Orbital Integrals

The Subregular Germ of Orbital Integrals

Author: Thomas Callister Hales

Publisher: American Mathematical Soc.

Published: 1992

Total Pages: 161

ISBN-13: 0821825399

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An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of asymptotic expansions. The integral formula is applied to the question of the transfer of a [italic small capital]K-orbital integral to an endoscopic group. It is shown that the quadratic characters arising in the subregular germs are compatible with the transfer. Details of the transfer are given for the subregular germ of unitary groups.


Book Synopsis The Subregular Germ of Orbital Integrals by : Thomas Callister Hales

Download or read book The Subregular Germ of Orbital Integrals written by Thomas Callister Hales and published by American Mathematical Soc.. This book was released on 1992 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integral formula for the subregular germ of a [italic small capital]K-orbital integral is developed. The formula holds for any reductive group over a [italic]p-adic field of characteristic zero. This expression of the subregular germ is obtained by applying Igusa's theory of asymptotic expansions. The integral formula is applied to the question of the transfer of a [italic small capital]K-orbital integral to an endoscopic group. It is shown that the quadratic characters arising in the subregular germs are compatible with the transfer. Details of the transfer are given for the subregular germ of unitary groups.

Lie Algebras, Vertex Operator Algebras, and Related Topics

Lie Algebras, Vertex Operator Algebras, and Related Topics

Author: Katrina Barron

Publisher: American Mathematical Soc.

Published: 2017-08-15

Total Pages: 274

ISBN-13: 1470426668

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This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.


Book Synopsis Lie Algebras, Vertex Operator Algebras, and Related Topics by : Katrina Barron

Download or read book Lie Algebras, Vertex Operator Algebras, and Related Topics written by Katrina Barron and published by American Mathematical Soc.. This book was released on 2017-08-15 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.

Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules

Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules

Author: Cristiano Husu

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 98

ISBN-13: 0821825712

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The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z2-twisted vertex operators are introduced and a Jacobi identity for these operators is established. Then these ideas are used to interpret and recover the twisted [bold capital]Z-operators and corresponding generating function identities developed by Lepowsky and R. L. Wilson. This work is closely related to the twisted parafermion algebra constructed by Zamolodchikov-Fateev.


Book Synopsis Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules by : Cristiano Husu

Download or read book Extensions of the Jacobi Identity for Vertex Operators, and Standard $A^{(1)}_1$-Modules written by Cristiano Husu and published by American Mathematical Soc.. This book was released on 1993 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main axiom for a vertex operator algebra (over a field of characteristic zero), the Jacobi identity, is extended to multi-operator identities. Then relative [bold capital]Z2-twisted vertex operators are introduced and a Jacobi identity for these operators is established. Then these ideas are used to interpret and recover the twisted [bold capital]Z-operators and corresponding generating function identities developed by Lepowsky and R. L. Wilson. This work is closely related to the twisted parafermion algebra constructed by Zamolodchikov-Fateev.

Unraveling the Integral Knot Concordance Group

Unraveling the Integral Knot Concordance Group

Author: Neal W. Stoltzfus

Publisher: American Mathematical Soc.

Published: 1977

Total Pages: 103

ISBN-13: 082182192X

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The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.


Book Synopsis Unraveling the Integral Knot Concordance Group by : Neal W. Stoltzfus

Download or read book Unraveling the Integral Knot Concordance Group written by Neal W. Stoltzfus and published by American Mathematical Soc.. This book was released on 1977 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a transfer construction, the integral Seifert matrices of knots whose Alexander polynomial is a power of a fixed irreducible polynomial are related to forms with the appropriate Hermitian symmetry on torsion free modules over an order in the algebraic number field determined by the Alexander polynomial. This group is then explicitly computed in terms of standard arithmetic invariants. In the symmetric case, this computation shows there are no elements of order four with an irreducible Alexander polynomial. Furthermore, the order is not necessarily Dedekind and non-projective modules can occur. The second level of invariants is given by constructing an exact sequence relating the global concordance group to the individual pieces described above. The integral concordance group is then computed by a localization exact sequence relating it to the rational group computed by J. Levine and a group of torsion linking forms.