Associative and Lie deformations of Poisson algebras

Elisabeth Remm

Communications in Mathematics (2012)

  • Volume: 20, Issue: 2, page 117-136
  • ISSN: 1804-1388

Abstract

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Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.

How to cite

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Remm, Elisabeth. "Associative and Lie deformations of Poisson algebras." Communications in Mathematics 20.2 (2012): 117-136. <http://eudml.org/doc/251397>.

@article{Remm2012,
abstract = {Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.},
author = {Remm, Elisabeth},
journal = {Communications in Mathematics},
keywords = {Poisson algebras; deformations; operads; cohomology; Poisson structures; deformations; Poisson cohomology},
language = {eng},
number = {2},
pages = {117-136},
publisher = {University of Ostrava},
title = {Associative and Lie deformations of Poisson algebras},
url = {http://eudml.org/doc/251397},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Remm, Elisabeth
TI - Associative and Lie deformations of Poisson algebras
JO - Communications in Mathematics
PY - 2012
PB - University of Ostrava
VL - 20
IS - 2
SP - 117
EP - 136
AB - Considering a Poisson algebra as a nonassociative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this nonassociative algebra. We give a natural interpretation of deformations which preserve the underlying associative structure and of deformations which preserve the underlying Lie algebra and we compare the associated cohomologies with the Poisson cohomology parametrizing the general deformations of Poisson algebras.
LA - eng
KW - Poisson algebras; deformations; operads; cohomology; Poisson structures; deformations; Poisson cohomology
UR - http://eudml.org/doc/251397
ER -

References

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