On Contractibility of Matrix Algebras

Abstract

. We show first that for each C*-algebra A, contractibility of A implies contractibility of M _n (A). We next prove that an incidence algebra A of upper triangular matrices, defined by a partially ordered set Ω on {1, 2,...,n} satisfying (p, q) ∈ Ω → p ≤ q, is a contractible Banach algebra iff there is no discordant couple of D-transitive triples of elements of Ω.