.svg){kind=logo}
LIE-RINEHART ALGEBRAS ON KAEHLER DIFFERENTIAL AND POISSON ALGEBRAS COHOMOLOGY
Keywords:
Poisson algebra, Poisson form, Lie-Rinehart algebra, differential algebra, modules of differential.DOI:
https://doi.org/10.17654/0972555524007Abstract
We establish that Poisson cohomology is precisely the cohomology of the Lie algebra $\Omega_{\mathbb{K}}(A)$ over $\mathbb{K}$ with coefficients in the adjoint representation of its Poisson module structure.
Received: October 27, 2023
Accepted: December 22, 2023
References
S. C. Gatsé, Some applications of Lie-Rinehart algebras, Palestinian Journal of Mathematics (to appear).
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.
E. Okassa, Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi, J. Pure Appl. Algebra 208 (2007), 1071-1089.
K. Mackenzie, General theory of Lie groupoids and Lie algebroids, London Mathematical Society Lecture Note Series, Vol. 213, Cambridge University Press, Cambridge, 2005.
J. Huebschmann, Lie-Rinehart algebras, descent, and quantization, fields, Inst. Commun. 3(43) (2004), 295-316.
J. Huebschmann, Poisson cohomology and quantization, J. Reine Angrew. Math. 408 (1999), 57-113.
I. Vaisman, Lectures on the geometry of Poisson manifolds, Progr. Math., Vol. 118, Birkhauser, Basel, 1994.
J.-L. Loday, Cyclic Homology, Springer, New York, Berlin, 1992.
K. H. Bhaskara and K. Viswanath, Poisson algebras and Poisson manifolds, Pitman Res. Notes in Math., Vol. 174, Longman, New York, 1988.
E. Kunz, Kaehler differentials, Vieweg Advanced Lectures in Mathematics, Braunschweig/Wiesbaden, Friedrich Vieweg and Sohn, 1986.
J. L. Koszul, Crochet de Schouten-Nijenhuis et cohomologie, Astérisque (hors série), Soc. Math. de France (1985), 257-271.
N. Bourbaki, Algèbre Chapitres 1 à 3, Hermann, Paris, 1970.
G. Rinehart, Differential forms for general commutative algebras, Trans. Amer. Math. Soc. 108 (1963), 195-222.
R. S. Palais, The cohomology of Lie rings, Amer. Math. Soc., Providence, R.I., Proc. Sympos. Pure Math., Vol. 3, 1961, pp. 130-137.
J.-C. Herz, Pseudo-algèbres de Lie, C. R. Acad. Sci. Paris 236 (1953), 1935-1937.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
