Supermatrix Representations of Semigroup Bands

摘要

Various semigroups of noninvertible supermatrices of the special(antitriangle) shape having nilpotent Berezinian which appear in supersymmetrictheories are defined and investigated. A subset of them continuously representsleft and right zero semigroups and rectangular bands. The ideal properties ofhigher order rectangular band analogs and the ``wreath'' version of them arestudied in detail. We introduce the ``fine'' equivalence relations leading to``multidimesional'' eggbox diagrams. They are full images of Green's relationson corresponding subsemigroups.