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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

References

1. Bourbaki, N., Algèbre homologique, Masson, Chapter X, Paris, 1980.Google Scholar
2. Brylinski, J. L., Some examples of Hochschild and cyclic homology, Lectures Notes in Math. 1271, Springer Verlag, 1987,33–72.Google Scholar
3. Feigin, B. and Tsygan, B., Additive K-Theory, Lectures Notes in Math. 1289(1987), 67–209.Google Scholar
4. Gong, D., Bivariant twisted cyclic theory and spectral sequences of crossed products, J. Pure Appl. Algebra 79(1992), 225–254.Google Scholar
5. Kassel, C., Cyclic homology of differential operators, the Virasoro algebra and a q-analogue, Comm. Math. Phys. (1992).Google Scholar
6. Kunz, E., Kahler differentials, Braunschweig: Wiesbaden Vieweg, 1986.Google Scholar
7. Mount, K. R. and Villamayor, O. E., Taylor series and higher derivations, Impresiones previas Dep. de Matemática, Univ. de Buenos Aires, 1969.Google Scholar
8. Nakai, Y., On the theory of differentials in commutative rings, J. Math. Soc. Japan (1) 13(1961), 63–84.Google Scholar
9. Nistor, V., Group cohomology and the cyclic homology of crossed products, Invent. Math. 99(1990), 411— 424.Google Scholar
10. Wodzicki, M., Cyclic homology of differential operators, Duke Math. J. 54(1987).Google Scholar