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.
2000 Mathematics Subject Classification:
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.