RESEARCH ARTICLE

Modular derivations for extensions of Poisson algebras

  • Shengqiang WANG
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  • Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Received date: 29 Nov 2015

Accepted date: 22 Feb 2016

Published date: 01 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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

Cite this article

Shengqiang WANG . Modular derivations for extensions of Poisson algebras[J]. Frontiers of Mathematics in China, 2017 , 12(1) : 209 -218 . DOI: 10.1007/s11464-016-0598-8

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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

DOI

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