FPM 2003, vol. 9, no. 3, pp. 111-123

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 3, PAGES 111-123

Conjugation properties in incidence algebras

V. E. Marenich

Abstract

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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 convex-diagonal function $f$ to be conjugated to the diagonal function $fe$ ; conditions under which the conjugacy $$ f \sim Ce + \zeta_{\lessdot} $$ holds (the function $$ Ce + \zeta_{\lessdot} $$ may be thought of as an analog for a Jordan box from matrix theory); a proof of the conjugation of two functions z_< and $$ \zeta_{\lessdot} $$ for partially ordered sets that satisfy the conditions mentioned above; an example of a partially ordered set for which the conjugacy $$ \zeta_< \sim \zeta_{\lessdot} $$ does not hold. These results involve conjugation criteria for convex-diagonal functions of some partially ordered sets.

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