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Conjugation properties in incidence algebras

Abstract

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 fCe + 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 gz -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.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 111–123, 2003.

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Marenich, V.E. Conjugation properties in incidence algebras. J Math Sci 135, 3341–3349 (2006). https://doi.org/10.1007/s10958-006-0163-1

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Keywords

  • Matrix Theory
  • Matrix Algebra
  • Full Matrix
  • Diagonal Function
  • Full Matrix Algebra