Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Kac-Moody Algebras and Applications

The Guest Editors for this special issue are

Richard Borcherds (University of California, Berkeley, USA)
Edward Frenkel (University of California, Berkeley, USA)
Victor Kac (Massachusetts Institute of Technology, USA)
Robert Moody (University of Victoria, Canada)
Jiri Patera (Université de Montréal, Canada)
Arturo Pianzola (University of Alberta, Canada)
Pierre Ramond (University of Florida, USA)

Kac–Moody algebras are named after independent papers by Victor Kac and Robert Moody both published in 1968. These algebras, especially affine Lie algebras, have various applications in theoretical and mathematical physics (for example in conformal field theory and theory of exactly solvable models), geometry, etc.

This special issue is devoted to 40th anniversary of Kac–Moody algebras.

The issue contains 20 papers with the total of 569 pages.

We would like to thank all the authors who have published papers in the issue, and to give our special thanks to all the referees for providing constructive reviews.

The Guest Editors        

Papers in this Issue:

Classification of Finite Dimensional Modular Lie Superalgebras with Indecomposable Cartan Matrix
Sofiane Bouarroudj, Pavel Grozman and Dimitry Leites
SIGMA 5 (2009), 060, 63 pages   [ abs   pdf   ps ]
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Luigi Accardi and Andreas Boukas
SIGMA 5 (2009), 056, 31 pages   [ abs   pdf   ps ]
Singularities of Affine Schubert Varieties
Jochen Kuttler and Venkatramani Lakshmibai
SIGMA 5 (2009), 048, 31 pages   [ abs   pdf   ps ]
Homological Algebra and Divergent Series
Vassily Gorbounov and Vadim Schechtman
SIGMA 5 (2009), 034, 31 pages   [ abs   pdf   ps ]
Vector Fields on the Space of Functions Univalent Inside the Unit Disk via Faber Polynomials
Helene Airault
SIGMA 5 (2009), 032, 11 pages   [ abs   pdf   ps ]
Induced Modules for Affine Lie Algebras
Vyacheslav Futorny and Iryna Kashuba
SIGMA 5 (2009), 026, 14 pages   [ abs   pdf   ps ]
The Group of Quasisymmetric Homeomorphisms of the Circle and Quantization of the Universal Teichmüller Space
Armen G. Sergeev
SIGMA 5 (2009), 015, 20 pages   [ abs   pdf   ps ]
Simple Finite Jordan Pseudoalgebras
Pavel Kolesnikov
SIGMA 5 (2009), 014, 17 pages   [ abs   pdf   ps ]
Self-Consistent-Field Method and τ-Functional Method on Group Manifold in Soliton Theory: a Review and New Results
Seiya Nishiyama, João da Providência, Constança Providência, Flávio Cordeiro and Takao Komatsu
SIGMA 5 (2009), 009, 76 pages   [ abs   pdf   ps ]
Quiver Varieties and Branching
Hiraku Nakajima
SIGMA 5 (2009), 003, 37 pages   [ abs   pdf   ps ]
The N = 1 Triplet Vertex Operator Superalgebras: Twisted Sector
Drazen Adamovic and Antun Milas
SIGMA 4 (2008), 087, 24 pages   [ abs   pdf   ps ]
Vertex Algebroids over Veronese Rings
Fyodor Malikov
SIGMA 4 (2008), 086, 28 pages   [ abs   pdf   ps ]
String Functions for Affine Lie Algebras Integrable Modules
Petr Kulish and Vladimir Lyakhovsky
SIGMA 4 (2008), 085, 18 pages   [ abs   pdf   ps ]
Generating Series for Nested Bethe Vectors
Sergey Khoroshkin and Stanislav Pakuliak
SIGMA 4 (2008), 081, 23 pages   [ abs   pdf   ps ]
Non-Gatherable Triples for Non-Affine Root Systems
Ivan Cherednik and Keith Schneider
SIGMA 4 (2008), 079, 12 pages   [ abs   pdf   ps ]
The PBW Filtration, Demazure Modules and Toroidal Current Algebras
Evgeny Feigin
SIGMA 4 (2008), 070, 21 pages   [ abs   pdf   ps ]
Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces
Doug Pickrell
SIGMA 4 (2008), 069, 33 pages   [ abs   pdf   ps ]
Wall Crossing, Discrete Attractor Flow and Borcherds Algebra
Miranda C.N. Cheng and Erik P. Verlinde
SIGMA 4 (2008), 068, 33 pages   [ abs   pdf   ps ]
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras
Dmitry Fuchs and Constance Wilmarth
SIGMA 4 (2008), 059, 11 pages   [ abs   pdf   ps ]
On Griess Algebras
Michael Roitman
SIGMA 4 (2008), 057, 35 pages   [ abs   pdf   ps ]

Special Issues in SIGMA

SIGMA main page