Free symmetric algebras in division rings generated by enveloping algebras of Lie algebras

Autor(es)

Ferreira, Vitor O. ^[1] ; Goncalves, Jairo Z. ^[1] ; Sanchez, Javier ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Math IME, BR-05314970 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 25, n. 6, p. 1075-1106, SEP 2015.
• Citações Web of Science: 2

Resumo

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 bar right arrow-x, can be extended to an involution of U(L), and Cimpric 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. (AU)

• Processo FAPESP: 09/52665-0 - Grupos, anéis e álgebras: interações e aplicações
• Beneficiário: Francisco Cesar Polcino Milies
• Modalidade de apoio: Auxílio à Pesquisa - Temático