On the *-minimality of algebras with involution

In Di Vincenzo and La Scala (2007) [1], given a n-tuple (A1,…,An) of finite dimensional *-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by R:=UT*(A1,…,An), was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its *-exponent is *-PI equivalent to R for a suitable choice of the algebras Ai. Motivated by a conjecture stated in the same paper, here we show that R is *-minimal when either it is *-symmetric or n=2.