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α-Derivations

Published online by Cambridge University Press:  20 November 2018

María Julia Redondo  and
Andrea Solotar
María Julia Redondo
Affiliation:
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Pabellón 1 Universidad de Buenos Aires, (1428), Buenos Aires, Argentina
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Abstract

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Let A be a commutative k-algebra with 1. We present a characterization of α-derivations, for α: A →> A a morphism of algebras, using α-Taylor series. When S = C[x,x-1,ξ] and α(x) = qx, α(ξ) = qξ, we compare the q-de Rham cohomology of the C-algebra S with the Hochschild homology of Dq, the algebra of q-difference operators on C[x,x-1], for q ∊ C, q ≠ 0,1.

Résumé

Résumé

Soient k et A deux anneux commutatifs unitaires, A une k-algèbre. Etant donné un endomorphisme α de l'algèbre A, nous montrons une caracterisation des α-dérivations en utilisant les α-séries de Taylor, dont nous prouvons certaines propriétés. Dans le cas particulier de l'algèbre Dq des operateurs q-differentiels sur C[x,x-1] nous faisons la comparaison entre la q-cohomologie de De Rham de C[x,x-1,ξ], et de homologie d'Hochschild de Dq, q ∊ C, q ≠ 0,1.

Keywords

16E4016U20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 481 - 489
Copyright
Copyright © Canadian Mathematical Society 1995

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