Star-group identities on units of group algebras: The non-torsion case

Author(s)

Giambruno, Antonio ^[1] ; Milies, Cesar Polcino ^[2] ; Sehgal, Sudarshan K. ^[3]

Affiliation

^[1] Univ Palermo, Dipartimento Matemat & Informat, Via Archirafi 34, I-90123 Palermo - Italy

^[2] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil

^[3] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1 - Canada

• Document type: Journal article
• Source: FORUM MATHEMATICUM; v. 30, n. 1, p. 213-225, JAN 2018.
• Web of Science Citations: 0

Abstract

Let G be a group, F a field and FG the corresponding group algebra. We consider an involution on FG which is the linear extension of an involution of G, e.g., g{*} = g(-1) for g is an element of G. This paper is focused on the characterization of a non-torsion group G provided the group of units U(FG) satisfies a {*}-group identity. The torsion case was studied in {[}7], and when {*} is the classical involution, this problem was solved in the case of symmetric units in {[}21]. (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