We show ¯rst that for each C*-algebra A, contractibility of A implies contractibility of Mn(A). We next prove that an incidence algebra A of upper triangular matrices, de¯ned by a partially ordered set ­ on f1; 2; : : : ; ng satisfying (p; q) 2 ­ ) p · q, is a contractible Banach algebra i® there is no discordant couple of D-transitive triples of elements of

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