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26 April 2024
 
  » arxiv » math-ph/9804013

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The Fuzzy Supersphere
Harald Grosse ; Gert Reiter ;
Date 21 Apr 1998
Journal Journal of Geometry and Physics 28, 349-383, 1998
Subject Mathematical Physics MSC-class: 17B56; 17B70; 46L87; 58A50; 58B30; 58C50; 81T60 | math-ph math.MP
AbstractWe introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative $Z_{2}$-graded algebras tending in a suitable limit to a dense subalgebra of the $Z_{2}$-graded algebra of ${cal H}^{infty}$-functions on the $(2| 2)$-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the "fuzzy level".
Source arXiv, math-ph/9804013
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