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

Location: http://mech.math.msu.su/~fpm/eng/k03/k033/k03308h.htm.