On the *-polynomial identities of a class of *-minimal algebras

摘要

Let F be an infinite field. We consider certain block-triangular algebras with involution U_n, with n ε N, having minimal *-exponent. We describe their *-polynomial identities, and in case char. F = 0, their structure as a T_*-ideal under the action of general linear groups. These goals are achieved by means of Y -proper polynomials. We also compute explicitly the irreducible modules occurring in the decomposition of B_Y (U_3) and their multiplicities.