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.

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 ]