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Group algebras whose symmetric and skew elements are Lie solvable
-
Gregory T. Lee
Published/Copyright:
June 15, 2009
Abstract
Let FG be the group algebra of a group G without 2-elements over a field F of characteristic p ≠ 2 endowed with the canonical involution induced from the map g ↦ g–1, g ∈ G. Let (FG)– and (FG)+ be the sets of skew and symmetric elements of FG, respectively, and let P denote the set of p-elements of G (with P = 1 if p = 0). In the present paper we prove that if either P is finite or G is non-torsion and (FG)– or (FG)+ is Lie solvable, then FG is Lie solvable. The remaining cases are also settled upon small restrictions.
Received: 2007-12-06
Accepted: 2008-01-27
Published Online: 2009-06-15
Published in Print: 2009-July
© de Gruyter 2009
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Articles in the same Issue
- The Noether Map I
- A general notion of algebraic entropy and the rank-entropy
- Computing the maximal algebra of quotients of a Lie algebra
- Mahler measure under variations of the base group
- Extremal α-pseudocompact abelian groups
- Group algebras whose symmetric and skew elements are Lie solvable
- Walks on graphs and lattices – effective bounds and applications
- Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions
- On the homotopy type of the non-completed classifying space of a p-local finite group
