Supermatrix Representations of Semigroup Bands

Details Supermatrix Representations of Semigroup Bands Supermatrix Representations of Semigroup Bands

1996-09-19

arxiv.org/abs/funct-an/9609002v1

Pure and Appl. Math. v.7 (1996) 235-261

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, Standard LaTeX with AmS fonts

Scientific paper

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

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