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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Ferreira, Vitor O. [1] ; Goncalves, Jairo Z. [1] ; Sanchez, Javier [1]
Total Authors: 3
Affiliation:
[1] Univ Sao Paulo, Dept Math IME, BR-05314970 Sao Paulo, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION; v. 25, n. 6, p. 1075-1106, SEP 2015.
Web of Science Citations: 2
Abstract

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)

FAPESP's process: 09/52665-0 - Groups, rings and algebras: interactions and applications
Grantee:Francisco Cesar Polcino Milies
Support Opportunities: Research Projects - Thematic Grants