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 $\$\; f\; \backslash sim\; Ce\; +\; \backslash zeta\_\{\backslash lessdot\}\; \$$
holds (the function $\$\; Ce\; +\; \backslash zeta\_\{\backslash lessdot\}\; \$$
may be thought of as an analog for a Jordan box from matrix
theory); a proof of the conjugation of two functions $$z_{<}
and $\$\; \backslash zeta\_\{\backslash lessdot\}\; \$$ for
partially ordered sets that satisfy the conditions mentioned above;
an example of a partially ordered set for which the
conjugacy $\$\; \backslash zeta\_<\; \backslash sim\; \backslash zeta\_\{\backslash lessdot\}\; \$$
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.

Last modified: January 24, 2005.