The fuzzy supersphere
Abstract
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative Z2-graded algebras tending in a suitable limit to a dense subalgebra of the Z2-graded algebra of H∞-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".
- Publication:
-
Journal of Geometry and Physics
- Pub Date:
- December 1998
- DOI:
- 10.1016/S0393-0440(98)00023-0
- arXiv:
- arXiv:math-ph/9804013
- Bibcode:
- 1998JGP....28..349G
- Keywords:
-
- Mathematical Physics;
- 17B56;
- 17B70;
- 46L87;
- 58A50;
- 58B30;
- 58C50;
- 81T60
- E-Print:
- 33 pages, LaTeX, some typos corrected