**Memoires de la Societe Mathematique de France**

Volume: 129;
2012;
99 pp;
Softcover

MSC: Primary 17; 14; 11; 19; 18;
**Print ISBN: 978-2-85629-349-2
Product Code: SMFMEM/129**

List Price: $48.00

Individual Member Price: $38.40

# Algèbres de Lie de Dimension Infinie et Théorie de la Descente

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*Wilhelm Alexander Steinmetz Zikesch*

A publication of the Société Mathématique de France

Let \(k\) be an algebraically closed field of
characteristic zero and let \(R\) be the Laurent polynomial
ring in two variables over \(k\). The main motivation behind
this work is a class of infinite dimensional Lie algebras over
\(k\), called *extended affine Lie algebras*
(EALAs). These algebras correspond to torsors under algebraic groups
over \(R\).

In this work the author classifies \(R\)-torsors under classical groups of large enough rank for outer type \(A\) and types \(B, C, D\), as well as for inner type \(A\) under stronger hypotheses. The author can thus deduce results on EALAs and also obtain a positive answer to a variant of Serre's Conjecture II for the ring \(R\): every smooth \(R\)-torsor under a semi-simple simply connected \(R\)-group of large enough rank of classical type \(B,C,D\) is trivial.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Table of Contents

# Table of Contents

## Algebres de Lie de Dimension Infinie et Theorie de la Descente

#### Readership

Graduate students and research mathematicians interested in Lie Algebras.