Modular derivations for extensions of Poisson algebras

Abstract

We compute explicitly the modular derivations for Poisson-Ore extensions and tensor products of Poisson algebras.

Keywords

Poisson algebra / Frobenius Poisson algebra / modular derivation / tensor Poisson algebra

References

[1] Ciccoli N. Poisson Ore extensions. In: Coen S, ed. Seminari di Geometria dell’Universit′a di Bologna 2005–2009. 2011

[2] Dolgushev V. The Van den Bergh duality and the modular symmetry of a Poisson variety. Selecta Math, 2009, 14: 199–228

[3] Huebschmann J. Duality for Lie-Rinehart algebras and the modular class. J Reine Angew Math, 1999, 510: 103–159

[4] Kontsevich M. Deformation quantization of Poisson manifolds. Lett Math Phys, 2003, 66: 157–216

[5] Laurent-Gengoux C, Pichereau A, Vanhaecke P. Poisson Structures. Grundlehren Math Wiss, Vol 347. Berlin: Springer, 2013

[6] Lichnerowicz A. Les varieties de Poisson et leurs algebres de Lie associees. J Differential Geom, 1977, 12: 253–300 (in French)

[7] Luo J, Wang S-Q, Wu Q-S. Twisted Poincar′e duality between Poisson homology and Poisson cohomology. J Algebra, 2015, 442: 484–505

[8] Oh S Q. Poisson polynomial rings. Comm Algebra, 2006, 34: 1265–1277

[9] Weibel C. An Introduction to Homological Algebra. Cambridge: Cambridge Univ Press, 1994

[10] Weinstein A. Lecture on Symplectic Manifolds. CBMS Reg Conf Ser Math, No 29. Providence: Amer Math Soc, 1977

[11] Zhu C, Van Oystaeyen F, Zhang Y-H. On (co)homology of Frobenius Poisson algebras. J K-Theory, 2014, 14: 371–386

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg