In Di Vincenzo and La Scala (2007) [1], 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 R := UT(*) (A(1), ... , A(n)), 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 A(i). Motivated by a conjecture stated in the same paper, here we show that R is *-minimal when either it is *-symmetric or n = 2. (C) 2009 Elsevier Inc. All rights reserved.
On the *-minimality of algebras with involution / Onofrio Mario Di, Vincenzo; Spinelli, Ernesto. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 323:1(2010), pp. 121-131. [10.1016/j.jalgebra.2009.09.038]
On the *-minimality of algebras with involution
SPINELLI, ERNESTO
2010
Abstract
In Di Vincenzo and La Scala (2007) [1], 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 R := UT(*) (A(1), ... , A(n)), 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 A(i). Motivated by a conjecture stated in the same paper, here we show that R is *-minimal when either it is *-symmetric or n = 2. (C) 2009 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
