Homology, Homotopy and Applications

Volume 4 (2002)

Number 2

The Roos Festschrift volume

A periodisation of semisimple Lie algebras

Pages: 337 – 355

DOI: http://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

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