Free symmetric pairs in the field of fractions of enveloping Lie algebras with involution

Autor(es)

Goncalves, Jairo Z.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. N/A, p. 13-pg., 2022-04-15.

Resumo

Let D be a division ring with center k, char k = p not equal 2, let * be an involution of D, and let D-dagger be the multiplicative group of D. A pair (u, v) is called free symmetric, if it is formed by symmetric elements, and it generates a free non-cyclic subgroup of D-dagger. If U(L) is the enveloping algebra of the non-abelian nilpotent Lie k-algebra L over the field k of characteristic not equal 2, and * is a k-involution of L extended to the field of fractions D of U(L), we show that D-dagger contains free symmetric pairs. We also discuss the consequences of symmetric elements of a normal subgroup being torsion over the center. (AU)

• Processo FAPESP: 15/09162-9 - Álgebra não comutativa e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático