Free symmetric group algebras in division rings generated by poly-orderable groups

2012/06/29 by Vitor O. Ferreira, Ferreira, Vitor O., Jairo Z. Goncalves +3
Mathematics · #16K40 #16S35 #16W10 (Primary) 16S10 #20F60 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16K40 #msc:16S10 #msc:16S35 #msc:16W10 #msc:20F60

paper · pdf · doi:10.48550/arxiv.1206.7013

18 pages

arxiv created 2012/06/29 · arxiv updated 2012/07/02

Abstract

We show that the canonical involution on a nonabelian poly-orderable group G extends to the Hughes-free division ring of fractions D of the group algebra k[G] of G over a field k and that, with respect to this involution, D contains a pair of symmetric elements freely generating a free group subalgebra of D over k.

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