A periodisation of semisimple Lie algebras

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

Full Text (PDF format)

Published 1 January 2002