Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras PDF Download
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Author: Shari A. Prevost
Publisher: American Mathematical Soc.
ISBN: 0821825275
Category : Mathematics
Languages : en
Pages : 113
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Book Description
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.
Author: Shari A. Prevost
Publisher: American Mathematical Soc.
ISBN: 0821825275
Category : Mathematics
Languages : en
Pages : 113
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Book Description
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.
Author: David Mitzman
Publisher: American Mathematical Soc.
ISBN: 0821850431
Category : Mathematics
Languages : en
Pages : 170
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Book Description
A revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Author: Daniel Ken Nakano
Publisher: American Mathematical Soc.
ISBN: 0821825305
Category : Mathematics
Languages : en
Pages : 97
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Book Description
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.
Author: Nirmala Prakash
Publisher: World Scientific Publishing Company
ISBN: 1911298240
Category : Science
Languages : en
Pages : 864
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Book Description
This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang-Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician. Contents:Complex Functions, Riemann Surfaces and Two-Dimensional Conformal Field Theory (an Introduction)Elements of Group Theory and Group RepresentationsA Primer on OperatorsBasics of Algebras and Related ConceptsInfinite-Dimensional AlgebrasThe Role of Symmetry in Physics and MathematicsAll That's Super — An IntroductionGravitation, Relativity and Black HolesBasics of Quantum TheoryTheory of Yang–Mills and the Yang–Mills–Higgs MechanismStrings and Superstrings (Elementary Aspects) Readership: Upper level undergraduates, graduate students, lecturers and researchers in theoretical physics, mathematical physics, quantum physics and astrophysics as well as Yang-Mills and superstring theory.
Author: Igor Frenkel
Publisher: American Mathematical Soc.
ISBN: 0821825550
Category : Mathematics
Languages : en
Pages : 79
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Book Description
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.
Author: Katrina Barron
Publisher: American Mathematical Soc.
ISBN: 1470426668
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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.
Author: Thomas Callister Hales
Publisher: American Mathematical Soc.
ISBN: 0821825399
Category : Mathematics
Languages : en
Pages : 161
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Book Description
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.
Author: Cristiano Husu
Publisher: American Mathematical Soc.
ISBN: 0821825712
Category : Mathematics
Languages : en
Pages : 98
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Book Description
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.
Author: Neal W. Stoltzfus
Publisher: American Mathematical Soc.
ISBN: 082182192X
Category : Mathematics
Languages : en
Pages : 103
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Book Description
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.
Author: Shirō Gotō
Publisher: American Mathematical Soc.
ISBN: 0821825844
Category : Mathematics
Languages : en
Pages : 149
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Book Description
At first, this volume was intended to be an investigation of symbolic blow-up rings for prime ideals defining curve singularities. The motivation for that has come from the recent 3-dimensional counterexamples to Cowsik's question, given by the authors and Watanabe: it has to be helpful, for further researches on Cowsik's question and a related problem of Kronecker, to generalize their methods to those of a higher dimension. However, while the study was progressing, it proved apparent that the framework of Part I still works, not only for the rather special symbolic blow-up rings but also in the study of Rees algebras R(F) associated to general filtrations F = {F[subscript]n} [subscript]n [subscript][set membership symbol][subscript bold]Z of ideals. This observation is closely explained in Part II of this volume, as a general ring-theory of Rees algebras R(F). We are glad if this volume will be a new starting point for the further researchers on Rees algebras R(F) and their associated graded rings G(F).
