Note on signed Brauer's algebras. (Q1887404)

Signed Brauer algebras \(\vec D_f(x)\) are introduced by \textit{M. Parvathi} and \textit{M. Kamaraj} [Commun. Algebra 26, No. 3, 839-855 (1998; Zbl 0944.16015)]. In the paper under review the authors realize certain homomorphic images of the signed Brauer algebras \(\vec D_f(n)\) as the centralizer of direct products of orthogonal groups and determine the values for which signed Brauer algebras \(\vec D_f(x)\) are semisimple.