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

Abstract

Let F be an infinite field, and let M n (F ) be the algebra of n × n matrices over F . Suppose that this algebra is equipped 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.