Abstract:
Various linear mappings of the incidence algebra $I(X, F)$of the partially ordered set $X$ over a field $F$ have always attracted attention of specialists. Automorphisms, isomorphisms, derivations, antiautomorphisms and involutions have been studied. Works that would study linear mappings of the incidence coalgebra$C_o(X, F)$ are unknown. This coalgebra is in some sense a dual object to the algebra $I(X, F)$. This paper reveals the structure of the automorphism group and the derivation space of the coalgebra $C_o(X, F)$. It is found that the group of automorphisms of the coalgebra Co(X, F) is antiisomorphic to the group of automorphisms of the algebra I(X, F), while the derivation spaces of these objects are isomorphic. The proofs are based on the well-known fact that the dual algebra to the coalgebra $C_o(X, F)$ is canonically isomorphic to the algebra $I(X, F)$. Acknowledgements The research of the second and third authors has been conducted at the expense of the Russian Science Foundation.
