eBook ISBN:  9780821881217 
Product Code:  CONM/442.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881217 
Product Code:  CONM/442.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 442; 2007; 474 ppMSC: Primary 17; 81; 82
The articles in this book are based on talks given at the international conference “Lie algebras, vertex operator algebras and their applications”, in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twentyfirst century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.
ReadershipGraduate students and research mathematicians interested in lie algebras, their representations, and generalizations.

Table of Contents

Lie algebras and related topics [ MR 2372580 ]

Karin Baur and Nolan Wallach — A class of gradings of simple Lie algebras [ MR 2372554 ]

Stephen Berman and Jun Morita — Conjugacy results for the Lie algebra $\mathfrak {sl}_2$ over an algebra which is a UFD [ MR 2372555 ]

Vyjayanthi Chari and Adriano Moura — KirillovReshetikhin modules associated to $G_2$ [ MR 2372556 ]

Rolf Farnsteiner — Support spaces and AuslanderReiten components [ MR 2372557 ]

Jörg Feldvoss — On the cohomology of modular Lie algebras [ MR 2372558 ]

Howard Garland — Eisenstein series on loop groups: MaassSelberg relations. IV [ MR 2372559 ]

Ayumu Hoshino — Generalized LittlewoodRichardson rule for exceptional Lie algebras $E_6$ and $F_4$ [ MR 2372560 ]

David Nacin — An introduction to $Q_n$ and its graph related quotients [ MR 2372561 ]

Toshiki Nakashima — Affine geometric crystal of type $G^{(1)}_2$ [ MR 2372562 ]

Florin F. Nichita and Deepak Parashar — New constructions of YangBaxter systems [ MR 2372563 ]

Vladimir Retakh, Shirlei Serconek and Robert Lee Wilson — Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials [ MR 2372564 ]

Alistair Savage — Geometric and combinatorial realizations of crystals of enveloping algebras [ MR 2372565 ]

H. Strade — Lie algebras of small dimension [ MR 2372566 ]

Vertex (operator) algebras and related topics [ MR 2372580 ]

I. I. Anguelova — Symmetric polynomials and $H_D$quantum vertex algebras [ MR 2372567 ]

Maarten J. Bergvelt — $H_T$vertex algebras [ MR 2372568 ]

Corina Calinescu — On intertwining operators and recursions [ MR 2372569 ]

Chongying Dong and Cuipo Jiang — Representations of vertex operator algebras [ MR 2372570 ]

Jürgen Fuchs — On nonsemisimple fusion rules and tensor categories [ MR 2372571 ]

Keith Hubbard — The duality between vertex operator algebras and coalgebras, modules and comodules [ MR 2372572 ]

James Lepowsky — Some developments in vertex operator algebra theory, old and new [ MR 2372573 ]

Haisheng Li — Twisted modules and quasimodules for vertex operator algebras [ MR 2372574 ]

Geoffrey Mason and Michael P. Tuite — Chiral algebras and partition functions [ MR 2372575 ]

Antun Milas — Modular forms and almost linear dependence of graded dimensions [ MR 2372576 ]

Mirko Primc — $(k,r)$admissible configurations and intertwining operators [ MR 2372577 ]

Zhenbo Qin and Weiqiang Wang — Hilbert schemes of points on the minimal resolution and soliton equations [ MR 2372578 ]

Christoph Schweigert, Jürgen Fuchs and Ingo Runkel — Twining characters and Picard groups in rational conformal field theory [ MR 2372579 ]


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The articles in this book are based on talks given at the international conference “Lie algebras, vertex operator algebras and their applications”, in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twentyfirst century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above.
Graduate students and research mathematicians interested in lie algebras, their representations, and generalizations.

Lie algebras and related topics [ MR 2372580 ]

Karin Baur and Nolan Wallach — A class of gradings of simple Lie algebras [ MR 2372554 ]

Stephen Berman and Jun Morita — Conjugacy results for the Lie algebra $\mathfrak {sl}_2$ over an algebra which is a UFD [ MR 2372555 ]

Vyjayanthi Chari and Adriano Moura — KirillovReshetikhin modules associated to $G_2$ [ MR 2372556 ]

Rolf Farnsteiner — Support spaces and AuslanderReiten components [ MR 2372557 ]

Jörg Feldvoss — On the cohomology of modular Lie algebras [ MR 2372558 ]

Howard Garland — Eisenstein series on loop groups: MaassSelberg relations. IV [ MR 2372559 ]

Ayumu Hoshino — Generalized LittlewoodRichardson rule for exceptional Lie algebras $E_6$ and $F_4$ [ MR 2372560 ]

David Nacin — An introduction to $Q_n$ and its graph related quotients [ MR 2372561 ]

Toshiki Nakashima — Affine geometric crystal of type $G^{(1)}_2$ [ MR 2372562 ]

Florin F. Nichita and Deepak Parashar — New constructions of YangBaxter systems [ MR 2372563 ]

Vladimir Retakh, Shirlei Serconek and Robert Lee Wilson — Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials [ MR 2372564 ]

Alistair Savage — Geometric and combinatorial realizations of crystals of enveloping algebras [ MR 2372565 ]

H. Strade — Lie algebras of small dimension [ MR 2372566 ]

Vertex (operator) algebras and related topics [ MR 2372580 ]

I. I. Anguelova — Symmetric polynomials and $H_D$quantum vertex algebras [ MR 2372567 ]

Maarten J. Bergvelt — $H_T$vertex algebras [ MR 2372568 ]

Corina Calinescu — On intertwining operators and recursions [ MR 2372569 ]

Chongying Dong and Cuipo Jiang — Representations of vertex operator algebras [ MR 2372570 ]

Jürgen Fuchs — On nonsemisimple fusion rules and tensor categories [ MR 2372571 ]

Keith Hubbard — The duality between vertex operator algebras and coalgebras, modules and comodules [ MR 2372572 ]

James Lepowsky — Some developments in vertex operator algebra theory, old and new [ MR 2372573 ]

Haisheng Li — Twisted modules and quasimodules for vertex operator algebras [ MR 2372574 ]

Geoffrey Mason and Michael P. Tuite — Chiral algebras and partition functions [ MR 2372575 ]

Antun Milas — Modular forms and almost linear dependence of graded dimensions [ MR 2372576 ]

Mirko Primc — $(k,r)$admissible configurations and intertwining operators [ MR 2372577 ]

Zhenbo Qin and Weiqiang Wang — Hilbert schemes of points on the minimal resolution and soliton equations [ MR 2372578 ]

Christoph Schweigert, Jürgen Fuchs and Ingo Runkel — Twining characters and Picard groups in rational conformal field theory [ MR 2372579 ]