In [Di Vincenzo, O.M., La Scala, R.: \emph{Minimal algebras with respect to their $\ast$-exponent}, J. Algebra 317 (2007), 642-657] given a $n$-tuple $(A_1,\ldots ,A_n)$ of finite dimensional $\ast$-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by $R:=UT_{\ast}(A_1, \ldots , A_n)$, was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its $\ast$-exponent is $\ast$-PI equivalent to $R$ for a suitable choice of the algebras $A_i$. Motivated by a conjecture stated in the same paper, here we show that $R$ is $\ast$-minimal when either it is $\ast$\emph{-symmetric} or $n=2$.
On the *-minimality of algebras with involution
SPINELLI, Ernesto
2010-01-01
Abstract
In [Di Vincenzo, O.M., La Scala, R.: \emph{Minimal algebras with respect to their $\ast$-exponent}, J. Algebra 317 (2007), 642-657] given a $n$-tuple $(A_1,\ldots ,A_n)$ of finite dimensional $\ast$-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by $R:=UT_{\ast}(A_1, \ldots , A_n)$, was introduced and it was proved that any finite dimensional algebra with involution which is minimal with respect to its $\ast$-exponent is $\ast$-PI equivalent to $R$ for a suitable choice of the algebras $A_i$. Motivated by a conjecture stated in the same paper, here we show that $R$ is $\ast$-minimal when either it is $\ast$\emph{-symmetric} or $n=2$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
