Generalized differential spaces with $d^N=0$ and the $q$-differential calculus

Details Generalized differential spaces with $d^N=0$ and the $q$-differential calculus Generalized differential spaces with $d^N=0$ and the $q$-differential calculus

1996-09-13

arxiv.org/abs/q-alg/9609012v1

Mathematics

Quantum Algebra

8 pages, Latex2e, uses pb-diagram, available at http://qcd.th.u-psud.fr, to be published in the Proceedings of the 5th Collo

Scientific paper

10.1007/BF01690337

We present some results concerning the generalized homologies associated with nilpotent endomorphisms $d$ such that $d^N=0$ for some integer $N\geq 2$. We then introduce the notion of graded $q$-differential algebra and describe some examples. In particular we construct the $q$-analog of the simplicial differential on forms, the $q$-analog of the Hochschild differential and the $q$-analog of the universal differential envelope of an associative unital algebra.

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