Abstract:
In the paper [6], we introduced Gram matrices
for the signed partition algebras, the algebra of Z2-relations and
the partition algebras. (s1, s2, r1, r2, p1, p2)-Stirling numbers of the
second kind are also introduced and their identities are established.
In this paper, we prove that the Gram matrix is similar to a matrix
which is a direct sum of block submatrices. As a consequence, the
semisimplicity of a signed partition algebra is established.
