Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

A periodisation of semisimple Lie algebras

Pages: 337 – 355

DOI: https://dx.doi.org/10.4310/HHA.2002.v4.n2.a16

Author

Anna Larsson (Department of Mathematics, Stockholm University, Sweden)

Abstract

In this text we study classical Lie algebras. We prove that a periodisation of such Lie algebras without $sl_2$-component can be presented as a free graded Lie algebra modulo quadratic relations only. Our approach will be through a Chevalley basis and our method relies on elementary tools only.

Keywords

Lie algebras, semisimple Lie algebras, quadratic relations, loop algebras, Chevalley basis

2010 Mathematics Subject Classification

17B20, 17B55, 17B67, 17B70

Published 1 January 2002