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.