Automorphisms and Higher Derivations of Incidence Algebras

AbstractLet I(P, A) be the incidence algebra of a locally finite pre-ordered set P over an algebra A. We derive decompositions of algebra maps I(P, A) → I(P, B) into simpler factors, under sufficient assumptions. As corollaries we deduce decompositions of algebra automorphisms and higher derivations of I(P, A), and we also formulate results in the special cases of upper triangular and full matrix algebras over A. This yields extensions of several older results of a similar type