On a type of matrix semigroup

Ponizovskiî, J. S.

doi:10.1007/bf02574331

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“…Here we study continuous supermatrix representations of idempotent operator semigroups firstly introduced in [12,13] for bands. Usually matrix semigroups are defined over a field K [14] (on some nonsupersymmetric generalizations of K-representations see [15,16]). But after discovery of supersymmetry [17,18] the realistic unified particle theories began to be considered in superspace [19,20].…”

Section: Introductionmentioning

confidence: 99%

On supermatrix idempotent operator semigroups

Duplij

2003

Linear Algebra and its Applications

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One-parameter semigroups of antitriangle idempotent supermatrices and corresponding superoperator semigroups are introduced and investigated. It is shown that t-linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives additional to exponential solution to the initial Cauchy problem. The corresponding functional equation and analog of resolvent are found for them. Differential and functional equations for idempotent (super)operators are derived for their general t power-type dependence. * E-mails: Steven.A.Duplij@univer.kharkov.ua and duplij@member.ams.org † Internet:

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