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 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.
KeywordsMatrix Theory Matrix Algebra Full Matrix Diagonal Function Full Matrix Algebra
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