Keywords and phrases: Poisson algebra, Poisson form, Lie-Rinehart algebra, differential algebra, modules of differential.
Received: October 27, 2023; Accepted: December 22, 2023; Published: February 5, 2024
How to cite this article: S. C. Gatse, A. M. Mavambou and O. M. Mikanou, Lie-Rinehart algebras on Kaehler differential and Poisson algebras cohomology, JP Journal of Algebra, Number Theory and Applications 63(2) (2024), 111-129. http://dx.doi.org/10.17654/0972555524007
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] S. C. Gatsé, Some applications of Lie-Rinehart algebras, Palestinian Journal of Mathematics (to appear). [2] S. C. Gatsé and C. C. Likouka, A Poisson algebra structure over the exterior algebra of a quadratic space, Advances in Mathematics: Scientific Journal 12(1) (2023), 175-186. [3] E. Okassa, Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi, J. Pure Appl. Algebra 208 (2007), 1071-1089. [4] K. Mackenzie, General theory of Lie groupoids and Lie algebroids, London Mathematical Society Lecture Note Series, Vol. 213, Cambridge University Press, Cambridge, 2005. [5] J. Huebschmann, Lie-Rinehart algebras, descent, and quantization, fields, Inst. Commun. 3(43) (2004), 295-316. [6] J. Huebschmann, Poisson cohomology and quantization, J. Reine Angrew. Math. 408 (1999), 57-113. [7] I. Vaisman, Lectures on the geometry of Poisson manifolds, Progr. Math., Vol. 118, Birkhauser, Basel, 1994. [8] J.-L. Loday, Cyclic Homology, Springer, New York, Berlin, 1992. [9] K. H. Bhaskara and K. Viswanath, Poisson algebras and Poisson manifolds, Pitman Res. Notes in Math., Vol. 174, Longman, New York, 1988. [10] E. Kunz, Kaehler differentials, Vieweg Advanced Lectures in Mathematics, Braunschweig/Wiesbaden, Friedrich Vieweg and Sohn, 1986. [11] J. L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Astérisque (hors série), Soc. Math. de France (1985), 257-271. [12] N. Bourbaki, Algèbre Chapitres 1 à 3, Hermann, Paris, 1970. [13] G. Rinehart, Differential forms for general commutative algebras, Trans. Amer. Math. Soc. 108 (1963), 195-222. [14] R. S. Palais, The cohomology of Lie rings, Amer. Math. Soc., Providence, R.I., Proc. Sympos. Pure Math., Vol. 3, 1961, pp. 130-137. [15] J.-C. Herz, Pseudo-algèbres de Lie, C. R. Acad. Sci. Paris 236 (1953), 1935-1937.
|