In a paper of Di Vincenzo and La Scala (2007) , given a n-tuple (A_1, . . . , A_n) of finite dimensional *-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by UT_*(A_1,…, A_n), was introduced. More precisely, in that paper it was proved that any finite dimensional algebra with involution which is minimal with respect to its *-exponent is *-PI equivalent to UT_*(A_1,…, A_n) for a suitable choice of the algebras A_i . Motivated by a conjecture stated in the same paper, here we show that UT_*(A_1,…, A_n) is *-minimal when either it is *-symmetric or n = 2.

On the *-minimality of algebras with involution

DI VINCENZO, Onofrio Mario;
2010-01-01

Abstract

In a paper of Di Vincenzo and La Scala (2007) , given a n-tuple (A_1, . . . , A_n) of finite dimensional *-simple algebras over a field of characteristic zero, a block-triangular matrix algebra with involution, denoted by UT_*(A_1,…, A_n), was introduced. More precisely, in that paper it was proved that any finite dimensional algebra with involution which is minimal with respect to its *-exponent is *-PI equivalent to UT_*(A_1,…, A_n) for a suitable choice of the algebras A_i . Motivated by a conjecture stated in the same paper, here we show that UT_*(A_1,…, A_n) is *-minimal when either it is *-symmetric or n = 2.
2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/2611
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