2014/06/11 by Vitor O. Ferreira, Jairo Z. Gonçalves, Ferreira, Vitor O. +3
Mathematics · Physics and Astronomy · #16S30 #16S36 #16W10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Primary 16K40 #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #Secondary 16S10 #math.RA #msc:16K40 #msc:16S10 #msc:16S30 #msc:16S36 #msc:16W10
paper · pdf · doi:10.48550/arxiv.1406.3078
arxiv created 2014/06/11 · openalex publication_date 2014/06/11 · arxiv updated 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any Lie algebra L over a field, its universal enveloping algebra U(L) can be embedded in a division ring D(L) constructed by Lichtman. If U(L) is an Ore domain, D(L) coincides with its ring of fractions. It is well known that the principal involution of L, x↦ -x, can be extended to an involution of U(L), and Cimpric has proved that this involution can be extended to one on D(L). For a large class of noncommutative Lie algebras L over a field of characteristic zero, we show that D(L) contains noncommutative free algebras generated by symmetric elements with respect to (the extension of) the principal involution. This class contains all noncommutative Lie algebras such that U(L) is an Ore domain.