Conjugation properties in incidence algebras

Incidence algebras can be regarded as a generalization of full matrix algebras. We present some conjugation properties for incidence functions. The list of results is as follows: a criterion for a convexdiagonal function f to be conjugated to the diagonal function fe; conditions under which the conjugacy f ∼ Ce + ζ <-holds (the function Ce + ζ < may be thought of as an analog for a Jordan box from matrix theory); a proof of the conjugation of two functions ζ < and ζ < for partially ordered sets that satisfy the conditions mentioned above; an example of a partially ordered set for which the conjugacy ζ < ∼ ζ < does not hold. These results involve conjugation criteria for convex-diagonal functions of some partially ordered sets. © 2006 Springer Science+Business Media, Inc.