On the *-Polynomial Identities of a Class of *-Minimal Algebras

Abstract

Let F be an infinite field. We consider certain block-triangular algebras with involution U _n , with n ∈ 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.

Key Words:

• Algebras with involution
• Cocharacters
• Polynomial identities
• Proper polynomials

2000 Mathematics Subject Classification:

• Primary 16R50
• Secondary 16R10

ACKNOWLEDGMENTS

The authors wish to thank the referee for his/her useful suggestions in improving some proofs and considerations. This article is partially supported by MIUR COFIN 2005 and Università\ di Bari.

Notes

Communicated by I. P. Shestakov.