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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2020; 57(1): 113-129

Online first article August 30, 2019      Printed January 1, 2020

https://doi.org/10.4134/JKMS.j180762

Copyright © The Korean Mathematical Society.

Cohomology ring of the tensor product of Poisson algebras

Can Zhu

University of Shanghai for Science and Technology

Abstract

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In this paper, we study the Poisson cohomology ring of the tensor product of Poisson algebras. Explicitly, it is proved that the Poisson cohomology ring of tensor product of two Poisson algebras is isomorphic to the tensor product of the respective Poisson cohomology ring of these two Poisson algebras as Gerstenhaber algebras.

Keywords: Poisson algebra, tensor product, Gerstenhaber algebra

MSC numbers: Primary 17B63, 18G60

Supported by: This work was nancially supported by NSFC #11771085 and #11871125, and by Shanghai Science and Technology Program #19ZR1434600.

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