Download or read book String Path Integral Realization of Vertex Operator Algebras written by Haruo Tsukada and published by American Mathematical Soc.. This book was released on 1991 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish relations between vertex operator algebras in mathematics and string path integrals in physics. In particular, we construct the basic representations of affine Lie algebras of [italic capitals]ÂD̂Ê-type using a method of string path integrals.
Download or read book Two Dimensional Conformal Geometry and Vertex Operator Algebras written by Yi-Zhi Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.
Download or read book Vertex Operator Algebras and the Monster written by Igor Frenkel and published by Academic Press. This book was released on 1989-05-01 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
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.
Download or read book Introduction to Vertex Operator Algebras and Their Representations written by James Lepowsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
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.
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.
Download or read book Introduction to Vertex Operator Superalgebras and Their Modules written by Xiaoping Xu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic study on the structures of vertex operator superalgebras and their modules. Related theories of self-dual codes and lattices are included, as well as recent achievements on classifications of certain simple vertex operator superalgebras and their irreducible twisted modules, constructions of simple vertex operator superalgebras from graded associative algebras and their anti-involutions, self-dual codes and lattices. Audience: This book is of interest to researchers and graduate students in mathematics and mathematical physics.
Download or read book Mathematical Perspectives on Theoretical Physics written by Nirmala Prakash and published by World Scientific Publishing Company. This book was released on 2003-09-02 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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.
Download or read book Duality and Definability in First Order Logic written by Michael Makkai and published by American Mathematical Soc.. This book was released on 1993 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a conservative pretopos morphism between Boolean pretoposes is canonically equivalent to the domain-pretopos. The descent theorem contains the Beth definability theorem for classical first order logic. Moreover, it gives, via the standard translation from the language of categories to symbolic logic, a new definability theorem for classical first order logic concerning set-valued functors on models, expressible in purely syntactical (arithmetical) terms.
Download or read book Semistability of Amalgamated Products and HNN Extensions written by Michael L. Mihalik and published by American Mathematical Soc.. This book was released on 1992 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.
Download or read book The Inverse Problem of the Calculus of Variations for Ordinary Differential Equations written by Ian Anderson and published by American Mathematical Soc.. This book was released on 1992 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores various aspects of the inverse problem of the calculus of variations for systems of ordinary differential equations. The main problem centres on determining the existence and degree of generality of Lagrangians whose system of Euler-Lagrange equations coicides with a given system of ordinary differential equations. The authors rederive the basic necessary and sufficient conditions of Douglas for second order equations and extend them to equations of higher order using methods of the variational bicomplex of Tulcyjew, Vinogradov, and Tsujishita. The authors present an algorithm, based upon exterior differential systems techniques, for solving the inverse problem for second order equations. a number of new examples illustrate the effectiveness of this approach.
Download or read book Abelian Coverings of the Complex Projective Plane Branched along Configurations of Real Lines written by Eriko Hironaka 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: This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.
Download or read book A Generalization of Riemann Mappings and Geometric Structures on a Space of Domains in C n written by Stephen Semmes and published by American Mathematical Soc.. This book was released on 1992 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: Similar in philosophy to the study of moduli spaces in algebraic geometry, the central theme of this book is that spaces of (pseudoconvex) domains should admit geometrical structures that reflect the complex geometry of the underlying domains in a natural way. With its unusual geometric perspective of some topics in several complex variables, this book appeals to those who view much of mathematics in broadly geometrical terms.
Download or read book Gorenstein Quotient Singularities in Dimension Three written by Stephen Shing-Toung Yau and published by American Mathematical Soc.. This book was released on 1993 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In chapter one we address the classification of finite subgroups of [italic capitals]SL([bold]3,[double-struck capital]C). This is followed by a general method to find invariant polynomials and their relations of finite subgroups of [italic capitals]GL([bold]3,[double-struck capital]C). Lastly, we recall some properties of quotient varieties and prove that [double-struck capital]C3/[italic capital]G has isolated singularities if and only if [italic capital]G is abelian and 1 is not an eigenvalue of g in [italic capital]G.
