Algèbres de Lie de dimension infinie et théorie de la descente / Wilhelm Alexander Steinmetz Zikesch.

Format:

Book

Author/Creator:

Steinmetz Zikesch, Wilhelm Alexander.

Series:

Mémoire (Société mathématique de France) ; nouv. sér., no 129.

Mémoire (Société mathématique de France)

Language:

English

French

Subjects (All):

Infinite dimensional Lie algebras.

Affine algebraic groups.

Physical Description:

99 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société mathématique de France, 2012.

Language Note:

In French, with abstract in both English and French.

Summary:

Let k be an algebraically closed field of characteristic zero and let R be a ring of Laurent polynomials in two variables over k. The main motivation behind this work is a class of Lie algebras of infinite dimension over k, called extended affine Lie algebras (EALAs). These algebras correspond to torsors under linear algebraic groups over R. In this work we classify R-torsors under the classical groups of rank large enough for outdoor types A, B, C, D and type A Interior under stronger assumptions. Thus, we can deduce results on EALAs. We also get an affirmative answer to a variant of Serre's conjecture II for the ring R: any smooth R-torsor under a group semisimple simply connected rank large enough conventional type B, C and D is trivial.

Contents:

1. Introduction

2. Généralités et préliminaires

3. Les conjectures

4. Le cas ¹A[subscipt n]₋₁ et les groupes orthogonaux

5. Le cas C[subscript n], les autres groupes du type D[subsript n] et le cas ²A[subscript n]

6. La conjecture B

A. Compatibilité de la théorie de Morita avec la sute spectrale de S. Gille.

Notes:

Includes bibliographical references (pages [95]-99).

ISBN:

9782856293492

2856293492

OCLC:

827976272