Universal $q$-differential calculus and $q$-analog of homological algebra

Abstract

We recall the definition of $q$-differential algebras and discuss some representative examples. In particular we construct the $q$-analog of the Hochschild coboundary. We then construct the universal $q$-differential envelope of a unital associative algebra and study its properties. The paper also contains general results on $d^N=0$.

24 pages, Latex2e, uses pb-diagram, available at http://qcd.th.u-psud.fr

References in corpus (1)

• On the q-analog of homological algebra

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