Letters in Mathematical Physics

, Volume 37, Issue 4, pp 385–396 | Cite as

On an alternative supermatrix reduction

  • Steven Duplij


We consider a nonstandard odd reduction of supermatrices (as compared with the standard even reduction) which arises in connection with the possible extension of manifold structure group reductions. The study was initiated by consideration of generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated together. They can be unified into some kind of ‘sandwich’ semigroups. We also define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.

Mathematics Subject Classifications (1991)

20Mxx 81Rxx 17Axx 

Key words

semigroup ideal supersymmetry supermatrices Cayley-Hamilton theorem 


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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Steven Duplij
    • 1
  1. 1.Physics DepartmentUniversity of KaiserslauternKaiserslauternGermany

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