Free Lie algebras and formal power series

✍ Scribed by R.M. Bryant

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 200 KB
• Volume: 253
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(02)00068-6

✦ Synopsis

Let G be a group and K a field. If V is a graded KG-module of the form

The isomorphism types of V and L(V ) may be described by the power series n 1 [V n ]t n and n 1 [L n (V )]t n with coefficients from the Green ring. The main object of study is the function on power series which maps [V n ]t n to [L n (V )]t n for every graded KG-module V . Closed formulae are given in certain cases, and these are closely related to character formulae of Brandt and others.