ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65, 2 (1996)
pp. 175-188

UNIVERSAL $q$-DIFFERENTIAL CALCULUS AND $q$-ANALOG OF HOMOLOGICAL ALGEBRA
M. DUBOIS-VIOLETTE\footnoteLaboratoire associe au Centre National de la Recherche Scientifique - URA D006.\hfill and R. KERNER\footnoteLaboratoire associe au Centre National de la Recherche Scientifique - URA D0769.\hfill

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 $d^N=0$.

AMS subject classification. 16E40
Keywords.

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