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Articles

A note on the duality between Poisson homology and cohomology

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Pages 4170-4175 | Received 14 Oct 2019, Accepted 11 Apr 2020, Published online: 04 May 2020

References

  • Berger, R., Pichereau, A. (2014). Calabi-Yau algebras viewed as deformations of Poisson algebras. Algebr. Represent. Theor. 17(3):735–773. DOI: 10.1007/s10468-013-9417-z.
  • Huebschmann, J. (1990). Poisson cohomology and quantization. J. Reine Angew. Math. 408:57–113.
  • Krähmer, U. (2007). Poincaré duality in Hochschild (co)homology. In: Vlaam, K., Wet, A. B., eds. New Techniques in Hopf Algebras and Graded Ring Theory. Brussels: Kunsten (KVAB), pp. 117–125.
  • Lambre, T., Meur, P. L. (2018). Duality for differential operators of Lie-Rinehart algebras. Pacific J. Math. 297(2):405–454. DOI: 10.2140/pjm.2018.297.405.
  • Launois, S., Richard, L. (2007). Twisted Poincaré duality for some quadratic Poisson algebras. Lett. Math. Phys. 79(2):161–174. DOI: 10.1007/s11005-006-0133-z.
  • Lü, J.-F., Wang, X., Zhuang, G.-B. (2015). Universal enveloping algebras of Poisson Hopf algebras. J. Algebra 426:92–136. DOI: 10.1016/j.jalgebra.2014.12.010.
  • Lü, J.-F., Wang, X., Zhuang, G.-B. (2017). Homological unimodularity and Calabi-Yau condition for Poisson algebras. Lett. Math. Phys. 107(9):1715–1740. DOI: 10.1007/s11005-017-0967-6.
  • Luo, J., Wang, S.-Q., Wu, Q.-S. (2015). Twisted Poincaré duality between Poisson homology and Poisson cohomology. J. Algebra 442:484–505. DOI: 10.1016/j.jalgebra.2014.08.023.
  • Oh, S.-Q. (1999). Poisson enveloping algebras. Commun. Algebra 27(5):2181–2186. DOI: 10.1080/00927879908826556.
  • Rinehart, G. S. (1963). Differential forms on general commutative algebras. Trans. Amer. Math. Soc. 108(2):195–222. DOI: 10.1090/S0002-9947-1963-0154906-3.
  • Towers, M. Poisson and Hochschild cohomology and the semiclassical limit. arXiv:1304.6003, preprint (2013).
  • Umirbaev, U. (2012). Universal enveloping algebras and universal derivations of Poisson algebras. J. Algebra 354(1):77–94. DOI: 10.1016/j.jalgebra.2012.01.003.

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