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 Lepowsky, J. (James)
 Boston : Birkhäuser, c2004.
 Description
 Book — xi, 318 p. ; 25 cm.
 Summary

 Preface. Introduction. Formal Calculus. Vertex Operator Algebras: The Axiomatic Basics . Modules. Vertex Algebras. Families of Vertex Operator Algebras. References. Index.
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QA326 .L48 2004  Unknown 
 Lepowsky, J. (James)
 Providence, R.I. : American Mathematical Society, c1985.
 Description
 Book — ix, 84 p. ; 25 cm.
 Summary

 The Lie algebra $A_1^(1)$ The category $\cal P_k$ The generalized commutation relations Relations for standard modules Basis of $\Omega_L$ for a standard module $L$ Schur functions Proof of linear independence Combinatorial formulas.
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QA252.3 .L47 1985  Available 
 Dong, Chongying, 1958
 Boston : Birkhäuser, c1993.
 Description
 Book — ix, 202 p. : ill. ; 25 cm.
 Summary

 1. Introduction.
 2. The setting.
 3. Relative untwisted vertex operators.
 4. Quotient vertex operators.
 5. A Jacobi identity for relative untwisted vertex operators.
 6. Generalized vertex operator algebras and their modules.
 7. Duality for generalized vertex operator algebras.
 8. Monodromy representations of braid groups.
 9. Generalized vertex algebras and duality.
 10. Tensor products.
 11. Intertwining operators.
 12. Abelian intertwining algebras, third cohomology and duality.
 13. Affine Lie algebras and vertex operator algebras.
 14. Zalgebras and parafermion algebras. References. List of frequentlyused symbols, in order of appearance.
 (source: Nielsen Book Data)
 Introduction.The Setting.Relative Untwisted Vertex Operators.Quotient Vertex Operators.A Jacobi Identity for Relative Untwisted Vertex Operators.Generalized Vertex Operator Algebras and Theory.Duality for Generalized Vertex Operator Algebras.Monodromy Representations of Braid Groups.Generalized Vertex Algebras and Duality.Tensor Products.Intertwining Operators.Abelian Intertwining Algebras, Third Cohomology and Duality.Affine Lie Algebras and Vertex Operator Algebras.Aalgebras and Parafermion Algebras.Bibliography.List of Frequentlyused symbols, in order of appearance.Index.
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The rapidlyevolving 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. They are mathematically precise counterparts of what are known in physics as chiral algebras, and in particular, they are intimately related to string theory and conformal field theory. Dong and Lepowsky have generalized the theory of vertex operator algebras in a systematic way at three successively more general levels, all of which incorporate onedimensional braid groups representations intrinsically into the algebraic structure: First, the notion of 'generalized vertex operator algebra' incorporates such structures as Zalgebras, parafermion algebras, and vertex operator super algebras. Next, what they term 'generalized vertex algebras' further encompass the algebras of vertex operators associated with rational lattices. Finally, the most general of the three notions, that of 'abelian intertwining algebra', also illuminates the theory of intertwining operator for certain classes of vertex operator algebras. The monograph is written in a n accessible and selfcontained 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.
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QA326 .D66 1993  Available 
 Dong, Chongying.
 Boston, MA : Birkhäuser Boston : Imprint : Birkhäuser, 1993.
 Description
 Book — 1 online resource (ix, 206 pages).
 Summary

 1 Introduction.
 2 The setting.
 3 Relative untwisted vertex operators.
 4 Quotient vertex operators.
 5 A Jacobi identity for relative untwisted vertex operators.
 6 Generalized vertex operator algebras and their modules.
 7 Duality for generalized vertex operator algebras.
 8 Monodromy representations of braid groups.
 9 Generalized vertex algebras and duality.
 10 Tensor products.
 11 Intertwining operators.
 12 Abelian intertwining algebras, third cohomology and duality.
 13 Affine Lie algebras and vertex operator algebras.
 14 Zalgebras and parafermion algebras. List of frequentlyused symbols, in order of appearance.
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 Gelfand, Israel M.
 Boston, MA : Birkhäuser Boston : Imprint : Birkhäuser, 1993.
 Description
 Book — 1 online resource (280 pages)
 Summary

 The Degeneracy of Two Spectral Sequences
 Hopf Algebra Structures for the Heisenberg Algebra: I
 Avalanches, Sandpiles and Tutte Decompositions
 On the Dimension and Degree of the Projective Dual Variety: A qAnalog of the KatzKleiman Formula
 Crofton Densities and Nonlocal Differentials
 On the Local Geometry of a Bihamiltonian Structure
 The Classical Polylogarithms, Algebraic KTheory and?F(N)
 A Brief History of the Sporadic Simple Groups
 Vertex Operator Algebras and Operads
 Representations of the Quantized Function Algebras, 2Categories and Zamolodchikov Tetrahedra Equation
 Formal (Non)Commutative Symplectic Geometry
 Constructible Functions, Lagrangian Cycles and Computational Geometry
 Quantum Groups and Perverse Sheaves. An Example
 Linearly Recursive Sequences, Witt Algebras and Quantum Groups
 Complexes of Connected Graphs.
6. Vertex operator algebras and the Monster [1988]
 Frenkel, Igor.
 Boston : Academic Press, c1988.
 Description
 Book — liii, 508 p. : ill. ; 24 cm.
 Summary

 Lie Algebras. Formal Calculus: Introduction. Realizations of sl(2) by Twisted Vertex Operators. Realizations of sl(2) by Untwisted Vertex Operators. Central Extensions. The Simple Lie Algebras An, Dn, En. Vertex Operator Realizations of An, Dn, En. General Theory of Untwisted Vertex Operators. General Theory of Twisted Vertex Operators. The Moonshine Module. Triality. The Main Theorem. Completion of the Proof. Appendix: Complex Realization of Vertex Operator Algebras. Bibliography. Index of frequently used symbols. Index.
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QA326 .F746  Unknown 
 Gindikin, S. G. (Semen Grigorʹevich)
 Boston, MA : Birkhäuser Boston, 1996.
 Description
 Book — 1 online resource (356 pages).
 Summary

 Positive Curvature, Macroscopic Dimension, Spectral Gaps, and Higher Signatures
 Geometric Construction of Polylogarithms, II
 A Note on Localization and the RiemannRoch Formula
 A Note on ODEs from Mirror Symmetry.
 Gelfand, Israel M.
 Boston, MA : Birkhäuser Boston, 1996.
 Description
 Book — 1 online resource (280 pages)
 Summary

 Questions and Answers about Geometric Evolution Processes and Crystal Growth
 Remarks on the Extatic Points of Plane Curves
 Gibbs Measures and QuasiPeriodic Solutions for Nonlinear Hamiltonian Partial Differential Equations
 Radon Transform and Functionals on the Spaces of Curves
 A Unified Method for Solving Linear and Nonlinear Evolution Equations and an Application to Integrable Surfaces
 Noncommutative Vieta Theorem and Symmetric Functions
 ChernSimons Classes and Cocycles on the Lie Algebra of the Gauge Group
 Cycles for Asymptotic Solutions and the Weyl Group
 Homology of Moduli of Curves and Commutative Homotopy Algebras
 Canonical States on the Group of Automorphisms of a Homogeneous Tree
 Second Quantization of the Wilson Loop
 The Homogeneous Complex MongeAmpère Equation and the Infinite Dimensional Versions of Classic Symmetric Spaces
 Novikov Inequalities for Vector Fields.
 Gindikin, S. G. (Semen Grigorʹevich)
 Boston, MA : Birkhäuser Boston, 1995.
 Description
 Book — 1 online resource (750 pages).
 Summary

 Volume I
 Connection Formulas in the qanalog de Rham Cohomology
 Lagrangian Models of Minimal Representations of E6, E7 and E8
 Trigonometric Solutions of the YangBaxter Equation, Nets, and Hypergeometric Functions
 Analogies between the Langlands Correspondence and Topological Quantum Field Theory
 'Forms' of the Principal Series for GLn
 Geometry of Determinants of Elliptic Operators
 Quantum Groups at v =?
 The Symplectic Operad
 Quadratic Unipotent Representations of padic Groups
 On the Master Field in Two Dimensions
 Physical Methods Applied to Donaldson Theory.
 Gindikin, S. G. (Semen Grigorʹevich)
 Boston, MA : Birkhäuser Boston, 1995.
 Description
 Book — 1 online resource (324 pages).
 Summary

 Connection Formulas in the qanalog de Rham Cohomology
 Lagrangian Models of Minimal Representations of E6, E7 and E8
 Trigonometric Solutions of the YangBaxter Equation, Nets, and Hypergeometric Functions
 Analogies between the Langlands Correspondence and Topological Quantum Field Theory
 'Forms' of the Principal Series for GLn
 Geometry of Determinants of Elliptic Operators
 Quantum Groups at v =?
 The Symplectic Operad
 Quadratic Unipotent Representations of padic Groups
 On the Master Field in Two Dimensions
 Physical Methods Applied to Donaldson Theory.
 Frenkel, Igor.
 Providence, RI : American Mathematical Society, 1993.
 Description
 Book — 64 p.
 Summary

 Introduction Vertex operator algebras Duality for vertex operator algebras Modules Duality for modules References.
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Shelved by Series title NO.494  Unknown 
 Cambridge, UK ; New York : Cambridge University Press, 2010.
 Description
 Book — xii, 403 p. ; 23 cm.
 Summary

 Preface Schedule of talks
 1. Characters of crossed modules and premodular categories Peter Bantay
 2. On the injectivity of the KudlaMillson lift and surjectivity of the Borcherds lift Jan Hendrik Bruinier and Jens Funke
 3. Ordered spanning sets for vertex operator algebras and their modules Geoffrey Buhl
 4. Friendly giant meets pointlike instantons? On a new conjecture by John McKay Anda Degeratu and Katrin Wendland
 5. Modularity of trace functions in orbifold theory for Zgraded vertex operator superalgebras Chongying Dong and Zhongping Zhao
 6. Twisted modules for vertex operator algebras Benjamin Doyon
 7. Vertex operators and sporadic groups John F. Duncan
 8. The algebraic meaning of being a Hauptmodul Terry Gannon
 9. Borcherds' proof of the ConwayNorton conjecture Elizabeth Jurisich
 10. On the connection of certain Lie algebras with vertex algebras Haisheng Li
 11. Vertex operators and arithmetic: how a single photon illuminates number theory Geoffrey Mason
 12. Rational vertex operator algebras and their orbifolds Geoffrey Mason
 13. Quasifinite algebras graded by Hamiltonian and vertex operator algebras Atushi Matsuo, Kiyokazu Nagatomo and Akihiro Tsuchiya
 14. On certain automorphic forms associated to rational vertex operator algebras Antun Milas
 15. Moonshine and group cohomology Charles B. Thomas
 16. Monstrous and generalized Moonshine and permutation orbifolds Michael P. Tuite
 17. New computations in the Monster Robert A. Wilson.
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QA343 .M73 2010  Unknown 
 Providence, R.I. : American Mathematical Society, c2007.
 Description
 Book — xxi, 474 p. : ill. ; 26 cm.
 Summary

 Lie algebras and related topics: A class of gradings of simple Lie algebras by K. Baur and N. Wallach Conjugacy results for the Lie algebra $\mathfrak{sl}_2$ over an algebra which is a UFD by S. Berman and J. Morita KirillovReshetikhin modules associated to $G_2$ by V. Chari and A. Moura Support spaces and AuslanderReiten components by R. Farnsteiner On the cohomology of modular Lie algebras by J. Feldvoss Eisenstein series on loop groups: MaassSelberg relations
 4 by H. Garland Generalized LittlewoodRichardson rule for exceptional Lie algebras $E_6$ and $F_4$ by A. Hoshino An introduction to $Q_n$ and its graph related quotients by D. Nacin Affine geometric crystal of type $G^{(1)}_2$ by T. Nakashima New constructions of YangBaxter systems by F. F. Nichita and D. Parashar Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials by V. Retakh, S. Serconek, and R. L. Wilson Geometric and combinatorial realizations of crystals of enveloping algebras by A. Savage Lie algebras of small dimension by H. Strade Vertex (operator) algebras and related topics: Symmetric polynomials and $H_D$quantum vertex algebras by I. I. Anguelova $H_T$vertex algebras by M. J. Bergvelt On intertwining operators and recursions by C. Calinescu Representations of vertex operator algebras by C. Dong and C. Jiang On nonsemisimple fusion rules and tensor categories by J. Fuchs The duality between vertex operator algebras and coalgebras, modules and comodules by K. Hubbard Some developments in vertex operator algebra theory, old and new by J. Lepowsky Twisted modules and quasimodules for vertex operator algebras by H. Li Chiral algebras and partition functions by G. Mason and M. P. Tuite Modular forms and almost linear dependence of graded dimensions by A. Milas $(k, r)$Admissible configurations and intertwining operators by M. Primc Hilbert schemes of points on the minimal resolution and soliton equations by Z. Qin and W. Wang Twining characters and Picard groups in rational conformal field theory by C. Schweigert, J. Fuchs, and I. Runkel.
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QA252.3 .L555 2007  Available 
 Providence, Rhode Island : American Mathematical Society, [2017]
 Description
 Book — vi, 274 pages ; 26 cm.
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QA252.3 .L5547 2017  Unknown 
15. Functional analysis on the eve of the 21st century [1995  1996]
 Boston : Birkhäuser, c1995c1996.
 Description
 Book — 2 v. : ill. ; 25 cm.
 Summary

 Preface.Speakers at Conference in Honor of I. M. Gelfand.Curriculum Vitae of I. M. Gelfand.List of Publications: 19871995.A Tribute of I. M. Gelfand.Connection Formulas in the qanalog de Rham Cohomolgy.Lagrangian Models of Minimal Representations of E6, E7, and E8.Trigonometric Solutions of the YangBaxter Equation, Nets, and Hypergeometric Functions.Analogies between the Langlands Correspondence and Topological Quantum Field Theory."Forms" of the Principal Series for GLn.Geometry of Determinants of Elliptic Operators.Quantum Groups at v=infinity.The Symplectic Operad.Quadratic Unipotent Representations of padic Groups.On the Master Field in Two Dimensions.Physical Methods Applied to Donaldson Theory.
 (source: Nielsen Book Data)
 Preface.Speakers at Conference in Honor of I. M. Gelfand.Curriculum Vitae of I. M. Gelfand.List of Publications: 19871995.A Tribute of I. M. Gelfand.Positive Curvature, Macroscopic Dimension, Spectral Gaps, and Higher Signatures.Geometric Construction of Polylogarithms, II.A Note on Localization and the RiemannRoch Formula.A Note of ODEs from Mirror Symmetry.
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QA321 .F856 1995 V.1  Available 
QA321 .F856 1995 V.2  Available 
16. Vertex operators in mathematics and physics [1985]
 New York : SpringerVerlag, c1985.
 Description
 Book — xiv, 482 p. : ill. ; 24 cm.
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QA252 .V47 1985  Available 
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