Minimal algebras with respect to their ∗-exponent

Given an m-tuple (A1,…,Am) of finite dimensional ∗-simple algebras we introduce a block-triangular matrix algebra with involution, denoted as UT∗(A1,…,Am), where each Ai can be embedded as ∗-algebra. We describe the T∗-ideal of R=UT∗(A1,…,Am) in terms of the ideals T∗(Ai) and prove that any algebra with involution which is minimal with respect to its ∗-exponent is ∗-PI equivalent to R for a suitable choice of (A1,…,Am). Moreover we show that if m=1 or Ai=F for all i then R itself is a ∗-minimal algebra. The assumption for the base field F is characteristic zero.