Free Group Algebras in Division Rings with Valuation II

Autor(es)

Sanchez, Javier ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Math, IME, Rua Matao 1010, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES; v. 72, n. 6, p. 1463-1504, DEC 2020.
• Citações Web of Science: 0

Resumo

We apply the filtered and graded methods developed in earlier works to find (noncommutative) free group algebras in division rings. If L is a Lie algebra, we denote by U(L) its universal enveloping algebra. P. M. Cohn constructed a division ring D-L that contains U(L). We denote by D(L) the division subring of D-L generated by U(L). Let k be a ueld of characteristic zero, and let L be a nonabelian Lie k-algebra. If either L is residually nilpotent or U(L) is an Ore domain, we show that D(L) contains (noncommutative) free group algebras. In those same cases, if L is equipped with an involution, we are able to prove that the free group algebra in D(L) can be chosen generated by symmetric elements in most cases. Let G be a nonabelian residually torsion-free nilpotent group, and let k(G) be the division subring of theMalcev-Neumann series ring generated by the group algebra k{[}G]. If G is equipped with an involution, we show that k(G) contains a (noncommutative) free group algebra generated by symmetric elements. (AU)

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