Geodesic
ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 303-313

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we prove that any Zinbiel algebra can be endowed with the structure of commutative algebra with divided powers. We introduce the notion of universal enveloping Zinbiel algebra of a commutative algebra with divided powers algebras. We prove that the free divided powers algebra on a free module M, is the divided powers sub-algebra generated by M, of the divided powers algebra induced by the free Zinbiel algebra on M. Finally, we construct a basis for the enveloping Zinbiel algebra.
DOI : 10.1017/S0017089509990358
Mots-clés : 17A32, 17A01, 13A99 
DOKAS, IOANNIS. ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 303-313. doi: 10.1017/S0017089509990358
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[1] 1.Berthelot, P. and Ogus, Arthur, Notes on Crystalline Cohomology, Annals of Mathematics Studies (Princeton University Press, 1978). Google Scholar

[2] 2.Cartan, H., Algèbres de Eilenberg-MacLane et homotopie, Seminaire Henri Cartan, 7ème année 1954-1955, 2ème éd. Ecole Normale Supérieure, Paris (1956). Google Scholar

[3] 3.Fresse, B., On the homotopy of simplicial algebras over an operad, Trans. Amer. Math. Soc. 352 (2000), 4113–4141. Google Scholar | DOI

[4] 4.Loday, J.-L., Cup-product for Leibniz cohomology and dual Leibniz algebras, Math. Scand. 77 (1995), 189–196. Google Scholar | DOI

[5] 5.Loday, J.-L., Cyclic Homology, Grundlehren der Mathematischen Wissenschaften, 301 (Springer-Verlag, Berlin, 1998). Google Scholar

[6] 6.Loday, J.-L., Dialgebras, in Dialgebras and related operads, Springer Lecture Notes in Math. (2001), 7–66. Google Scholar

[7] 7.Loday, J.-L., Scindement d' associativité et algèbres de Hopf. Proceedings of the colloquium dedicated to the memory of Jean Leray, Nantes, France, June 17–18, 2002. Paris: Societe Mathematique de France. Seminaires et Congres , 155–172 (2004). Google Scholar

[8] 8.Reutenauer, C., Free Lie algebras, London Math. Soc. Monos. (N.S), No. 7 (Oxford Univ. Press, 1993). Google Scholar

[9] 9.Roby, N., Les algèbres à puissances divisées, Bull. Sc.math. Série 2, t. 89 (1965), 75–91. Google Scholar

[10] 10.Roby, N., Lois polynomes et lois formelles en théorie des modules, Annales scientifiques de l' E.N.S. 3 serie, tome 80, num. 3 (1963), 213–348. Google Scholar

[11] 11.Roby, N., Construction de certain algèbres à puissances divisées, Bull. Soc. Math. France 96 (1968), 97–113. Google Scholar

[12] 12.Soublin, J.-P., Puissances divisées caractéristique non nulle, Journal of Algebra 110 (1987), 523–529. Google Scholar | DOI

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