Graded polynomial Identities for matrices with the transpose involution over an infinite field

Author(s)

Goncalves Fonseca, Luis Felipe ^[1] ; de Mello, Thiago Castilho ^[2]

Affiliation

^[1] Univ Fed Vicosa, Inst Ciencias Exatas & Tecnol, Florestal, MG - Brazil

^[2] Univ Fed Sao Paulo, Inst Ciencia & Tecnol, BR-12231280 Sao Jose Dos Campos, SP - Brazil

• Document type: Journal article
• Source: COMMUNICATIONS IN ALGEBRA; v. 46, n. 4, p. 1630-1640, 2018.
• Web of Science Citations: 0

Abstract

Let F be an infinite field and let M-n (F) be the algebra of n x n matrices over F endowed with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of M-n (F) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature, which were obtained for the field of complex numbers and for a particular class of elementary G-gradings. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 14/10352-4 - Algebras matrices and varieties
• Grantee: Thiago Castilho de Mello
• Support Opportunities: Regular Research Grants