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Journal articles on the topic 'Poisson algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bavula, V. V. "The generalized Weyl Poisson algebras and their Poisson simplicity criterion." Letters in Mathematical Physics 110, no. 1 (2019): 105–19. http://dx.doi.org/10.1007/s11005-019-01214-7.

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Abstract A new large class of Poisson algebras, the class of generalized Weyl Poisson algebras, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl algebras. A Poisson simplicity criterion is given for generalized Weyl Poisson algebras, and an explicit description of the Poisson centre is obtained. Many examples are considered (e.g. the classical polynomial Poisson algebra in 2n variables is a generalized Weyl Poisson algebra).

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2

Ait Ben Haddou, Malika, Saïd Benayadi, and Said Boulmane. "Malcev–Poisson–Jordan algebras." Journal of Algebra and Its Applications 15, no. 09 (2016): 1650159. http://dx.doi.org/10.1142/s0219498816501590.

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Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to classify the Jordan structure ∘ on the underlying vector space of [Formula: see text] such that [Formula: see text] is an MPJ-algebra (∘ is called an MPJ-structure on Malcev algebra [Formula: see text]. In this paper we explicitly give all MPJ-s

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3

LI, HAISHENG. "VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS." Communications in Contemporary Mathematics 06, no. 01 (2004): 61–110. http://dx.doi.org/10.1142/s0219199704001264.

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This paper studies certain relations among vertex algebras, vertex Lie algebras and vertex Poisson algebras. In this paper, the notions of vertex Lie algebra (conformal algebra) and vertex Poisson algebra are revisited and certain general construction theorems of vertex Poisson algebras are given. A notion of filtered vertex algebra is formulated in terms of a notion of good filtration and it is proved that the associated graded vector space of a filtered vertex algebra is naturally a vertex Poisson algebra. For any vertex algebra V, a general construction and a classification of good filtrati

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4

Safronov, Pavel. "Braces and Poisson additivity." Compositio Mathematica 154, no. 8 (2018): 1698–745. http://dx.doi.org/10.1112/s0010437x18007212.

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We relate the brace construction introduced by Calaque and Willwacher to an additivity functor. That is, we construct a functor from brace algebras associated to an operad${\mathcal{O}}$to associative algebras in the category of homotopy${\mathcal{O}}$-algebras. As an example, we identify the category of$\mathbb{P}_{n+1}$-algebras with the category of associative algebras in$\mathbb{P}_{n}$-algebras. We also show that under this identification there is an equivalence of two definitions of derived coisotropic structures in the literature.

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5

Changjian, Fu, and Peng Lian'gang. "Hall algebras as Poisson algebras." SCIENTIA SINICA Mathematica 48, no. 11 (2018): 1673. http://dx.doi.org/10.1360/n012017-00268.

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6

Loose, Frank. "Symplectic algebras and poisson algebras." Communications in Algebra 21, no. 7 (1993): 2395–416. http://dx.doi.org/10.1080/00927879308824682.

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7

Chtioui, T., S. Mabrouk, and A. Makhlouf. "Hom–Jordan–Malcev–Poisson algebras." Ukrains’kyi Matematychnyi Zhurnal 74, no. 11 (2022): 1571–82. http://dx.doi.org/10.37863/umzh.v74i11.6360.

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UDC 512.5 We provide and study a Hom-type generalization of Jordan–Malcev–Poisson algebras called Hom–Jordan–Malcev–Poisson algebras. We show that they are closed under twisting by suitable self-maps and give a characterization of admissible Hom–Jordan–Malcev–Poisson algebras. In addition, we introduce the notion of pseudo-Euclidian Hom–Jordan–Malcev–Poisson algebras and describe its T * -extension. Finally, we generalize the notion of Lie–Jordan–Poisson triple system to the Hom setting and establish its relationships with Hom–Jordan–Malcev–Poisson algebras.

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8

OKASSA, EUGÈNE. "ON LIE–RINEHART–JACOBI ALGEBRAS." Journal of Algebra and Its Applications 07, no. 06 (2008): 749–72. http://dx.doi.org/10.1142/s0219498808003107.

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We show that Jacobi algebras (Poisson algebras respectively) can be defined only as Lie–Rinehart–Jacobi algebras (as Lie–Rinehart–Poisson algebras respectively). Also we show that contact manifolds, locally conformal symplectic manifolds (symplectic manifolds respectively) can be defined only as symplectic Lie–Rinehart–Jacobi algebras (only as symplectic Lie–Rinehart–Poisson algebras respectively). We define symplectic Lie algebroids.

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9

Hu, Xianguo. "Universal enveloping Hom-algebras of regular Hom-Poisson algebras." AIMS Mathematics 7, no. 4 (2022): 5712–27. http://dx.doi.org/10.3934/math.2022316.

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<abstract><p>In this paper, we introduce universal enveloping Hom-algebras of Hom-Poisson algebras. Some properties of universal enveloping Hom-algebras of regular Hom-Poisson algebras are discussed. Furthermore, in the involutive case, it is proved that the category of involutive Hom-Poisson modules over an involutive Hom-Poisson algebra $ A $ is equivalent to the category of involutive Hom-associative modules over its universal enveloping Hom-algebra $ U_{eh}(A) $.</p></abstract>

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10

Kolesnikov, P. S. "Universal enveloping Poisson conformal algebras." International Journal of Algebra and Computation 30, no. 05 (2020): 1015–34. http://dx.doi.org/10.1142/s0218196720500289.

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Lie conformal algebras are useful tools for studying vertex operator algebras and their representations. In this paper, we establish close relations between Poisson conformal algebras and representations of Lie conformal algebras. We also calculate explicitly Poisson conformal brackets on the associated graded conformal algebras of universal associative conformal envelopes of the Virasoro conformal algebra and the Neveu–Schwartz conformal superalgebra.

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11

Xu, Ping. "Noncommutative Poisson Algebras." American Journal of Mathematics 116, no. 1 (1994): 101. http://dx.doi.org/10.2307/2374983.

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12

Oh, Sei-Qwon. "Poisson enveloping algebras." Communications in Algebra 27, no. 5 (1999): 2181–86. http://dx.doi.org/10.1080/00927879908826556.

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13

Mishchenko, S. P., V. M. Petrogradsky, and A. Regev. "Poisson PI algebras." Transactions of the American Mathematical Society 359, no. 10 (2007): 4669–95. http://dx.doi.org/10.1090/s0002-9947-07-04008-1.

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14

Van den Bergh, Michel. "Double Poisson algebras." Transactions of the American Mathematical Society 360, no. 11 (2008): 5711–69. http://dx.doi.org/10.1090/s0002-9947-08-04518-2.

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15

Arnlind, Joakim, and Ahmed Al-Shujary. "Kähler–Poisson algebras." Journal of Geometry and Physics 136 (February 2019): 156–72. http://dx.doi.org/10.1016/j.geomphys.2018.11.001.

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16

Bao, Yan-Hong, Yu Ye, and James Zhang. "Restricted Poisson algebras." Pacific Journal of Mathematics 289, no. 1 (2017): 1–34. http://dx.doi.org/10.2140/pjm.2017.289.1.

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17

Luo, Juan, Shengqiang Wang, and Quanshui Wu. "Frobenius Poisson algebras." Frontiers of Mathematics in China 14, no. 2 (2019): 395–420. http://dx.doi.org/10.1007/s11464-019-0756-x.

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18

Xu, Xiaoping. "Novikov–Poisson Algebras." Journal of Algebra 190, no. 2 (1997): 253–79. http://dx.doi.org/10.1006/jabr.1996.6911.

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19

Yao, Yuan, Yu Ye, and Pu Zhang. "Quiver Poisson algebras." Journal of Algebra 312, no. 2 (2007): 570–89. http://dx.doi.org/10.1016/j.jalgebra.2007.03.034.

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20

Ratseev, S. M. "COMMUTATIVE LEIBNIZ-POISSON ALGEBRAS OF POLYNOMIAL GROWTH." Vestnik of Samara University. Natural Science Series 18, no. 3.1 (2017): 54–65. http://dx.doi.org/10.18287/2541-7525-2012-18-3.1-54-65.

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In this paper we study commutative Leibniz-Poisson algebras. We prove that a variety of commutative Leibniz-Poisson algebras has either polynomial growth or growth with exponential not less than 2, the ﬁeld being arbitrary. We prove that every variety of commutative Leibniz-Poisson algebras of polynomial growth over a ﬁeld of characteristic 0 has a ﬁnite basis for its polynomial identities. Also we construct a variety of commutative Leibniz-Poisson algebras with almost polynomial growth.

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21

Kosmann-Schwarzbach, Yvette. "From Poisson algebras to Gerstenhaber algebras." Annales de l’institut Fourier 46, no. 5 (1996): 1243–74. http://dx.doi.org/10.5802/aif.1547.

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22

Huang, Junyuan, Xueqing Chen, Zhiqi Chen, and Ming Ding. "On a conjecture on transposed Poisson $ n $-Lie algebras." AIMS Mathematics 9, no. 3 (2024): 6709–33. http://dx.doi.org/10.3934/math.2024327.

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<abstract><p>The notion of a transposed Poisson $ n $-Lie algebra has been developed as a natural generalization of a transposed Poisson algebra. It was conjectured that a transposed Poisson $ n $-Lie algebra with a derivation gives rise to a transposed Poisson $ (n+1) $-Lie algebra. In this paper, we focus on transposed Poisson $ n $-Lie algebras. We have obtained a rich family of identities for these algebras. As an application of these formulas, we provide a construction of $ (n+1) $-Lie algebras from transposed Poisson $ n $-Lie algebras with derivations under a certain strong

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23

Zakharov, A. S. "Embedding Novikov–Poisson algebras in Novikov–Poisson algebras of vector type." Algebra and Logic 52, no. 3 (2013): 236–49. http://dx.doi.org/10.1007/s10469-013-9237-6.

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24

Artemovych, Orest D., Anatolij K. Prykarpatski, and Denis L. Blackmore. "Examples of Lie and Balinsky-Novikov algebras related to Hamiltonian operators." Topological Algebra and its Applications 6, no. 1 (2018): 43–52. http://dx.doi.org/10.1515/taa-2018-0005.

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Abstract We study algebraic properties of Poisson brackets on non-associative non-commutative algebras, compatible with their multiplicative structure. Special attention is paid to the Poisson brackets of the Lie-Poisson type, related with the special Lie-structures on the differential-topological torus and brane algebras, generalizing those studied before by Novikov-Balinsky and Gelfand-Dorfman. Illustrative examples of Lie and Balinsky-Novikov algebras are discussed in detail. The non-associative structures (induced by derivation and endomorphism) of commutative algebras related to Lie and B

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25

Su, Yucai. "Poisson Brackets and Structure of Nongraded Hamiltonian Lie Algebras Related to Locally-Finite Derivations." Canadian Journal of Mathematics 55, no. 4 (2003): 856–96. http://dx.doi.org/10.4153/cjm-2003-036-7.

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AbstractXu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson algebras are isomorphic. Furthermore, the derivation algebras and the second cohomology groups are determined.

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26

Agore, Ana, Li Guo, Ivan Kaygorodov, and Stéphane Launois. "Mini-Workshop: Poisson and Poisson-type algebras." Oberwolfach Reports 20, no. 4 (2024): 2681–715. http://dx.doi.org/10.4171/owr/2023/46.

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27

Burde, Dietrich, and Christof Ender. "Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras." Linear Algebra and its Applications 584 (January 2020): 107–26. http://dx.doi.org/10.1016/j.laa.2019.09.010.

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28

Fehlberg Júnior, R., and I. Kaygorodov. "On the Kantor product, II." Carpathian Mathematical Publications 14, no. 2 (2022): 543–63. http://dx.doi.org/10.15330/cmp.14.2.543-563.

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We describe the Kantor square (and Kantor product) of multiplications, extending the classification proposed in [J. Algebra Appl. 2017, 16 (9), 1750167]. Besides, we explicitly describe the Kantor square of some low dimensional algebras and give constructive methods for obtaining new transposed Poisson algebras and Poisson-Novikov algebras; and for classifying Poisson structures and commutative post-Lie structures on a given algebra.

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29

Turusbekova, U., and G. Azieva. "The automorphism group of Poisson algebras on k[x, y]." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 87, no. 3 (2017): 117–24. http://dx.doi.org/10.31489/2017m3/117-124.

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Poisson algebras play a key role in the Hamiltonian mechanics, symplectic geometry and also are central in the study of quantum groups. At present, Poisson algebras are investigated by the many mathematicians of Russia, France, the USA, Brazil, Argentina, Bulgaria etc. The purpose of the present paper is to describe the automorphism groups of polynomial algebras endowed with additional structure, namely, with Poisson brackets. For any f∈k[x,y] one can transform associative-commutative algebra k[x,y] into a Poisson algebra Pf by defining a Poisson bracket by the rule {x, y}=f. Obviously, a stru

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30

Zhu, Can, Fred Van Oystaeyen, and Yinhuo Zhang. "On (co)homology of Frobenius Poisson algebras." Journal of K-Theory 14, no. 2 (2014): 371–86. http://dx.doi.org/10.1017/is014007026jkt276.

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AbstractIn this paper, we study Poisson (co)homology of a Frobenius Poisson algebra. More precisely, we show that there exists a duality between Poisson homology and Poisson cohomology of Frobenius Poisson algebras, similar to that between Hochschild homology and Hochschild cohomology of Frobenius algebras. Then we use the non-degenerate bilinear form on a unimodular Frobenius Poisson algebra to construct a Batalin-Vilkovisky structure on the Poisson cohomology ring making it into a Batalin-Vilkovisky algebra.

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31

NGAKEU, FERDINAND. "GRADED POISSON STRUCTURES AND SCHOUTEN–NIJENHUIS BRACKET ON ALMOST COMMUTATIVE ALGEBRAS." International Journal of Geometric Methods in Modern Physics 09, no. 05 (2012): 1250042. http://dx.doi.org/10.1142/s0219887812500429.

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We introduce and study the notion of abelian groups graded Schouten–Nijenhuis bracket on almost commutative algebras and show that any Poisson bracket on such algebras is defined by a graded bivector as in the classical Poisson manifolds. As a particular example, we introduce and study symplectic structures on almost commutative algebras. Our result is a generalization of the ℤ2-graded (super)-Poisson structures.

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32

CHO, EUN-HEE, and SEI-QWON OH. "SKEW ENVELOPING ALGEBRAS AND POISSON ENVELOPING ALGEBRAS." Communications of the Korean Mathematical Society 20, no. 4 (2005): 649–55. http://dx.doi.org/10.4134/ckms.2005.20.4.649.

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33

Lü, Jiafeng, Xingting Wang, and Guangbin Zhuang. "Universal enveloping algebras of Poisson Hopf algebras." Journal of Algebra 426 (March 2015): 92–136. http://dx.doi.org/10.1016/j.jalgebra.2014.12.010.

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34

Enriquez, Benjamin, and Gilles Halbout. "Poisson algebras associated to quasi-Hopf algebras." Advances in Mathematics 186, no. 2 (2004): 363–95. http://dx.doi.org/10.1016/j.aim.2003.08.007.

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35

Ratseev, S. M. "On minimal Poisson algebras." Russian Mathematics 59, no. 11 (2015): 54–61. http://dx.doi.org/10.3103/s1066369x15110067.

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36

Agore, Ana, and Gigel Militaru. "Jacobi and Poisson algebras." Journal of Noncommutative Geometry 9, no. 4 (2015): 1295–342. http://dx.doi.org/10.4171/jncg/224.

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37

Farkas, Daniel R. "Characterizations of poisson algebras." Communications in Algebra 23, no. 12 (1995): 4669–86. http://dx.doi.org/10.1080/00927879508825493.

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38

SU, Yucai. "Central simple Poisson algebras." Science in China Series A 41, no. 2 (2004): 245. http://dx.doi.org/10.1360/02ys0277.

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39

Siciliano, Salvatore, and Hamid Usefi. "Solvability of Poisson algebras." Journal of Algebra 568 (February 2021): 349–61. http://dx.doi.org/10.1016/j.jalgebra.2020.10.012.

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40

Farkas, Daniel R. "Modules for poisson algebras." Communications in Algebra 28, no. 7 (2000): 3293–306. http://dx.doi.org/10.1080/00927870008827025.

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41

Casas, J. M., and T. Datuashvili. "Noncommutative Leibniz–Poisson Algebras." Communications in Algebra 34, no. 7 (2006): 2507–30. http://dx.doi.org/10.1080/00927870600651091.

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42

Yang, Yan Hong, Yuan Yao, and Yu Ye. "(Quasi-)Poisson enveloping algebras." Acta Mathematica Sinica, English Series 29, no. 1 (2012): 105–18. http://dx.doi.org/10.1007/s10114-012-1041-z.

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43

Asif, Sania, and Yao Wang. "Constructing and Analyzing BiHom-(Pre-)Poisson Conformal Algebras." Symmetry 16, no. 11 (2024): 1533. http://dx.doi.org/10.3390/sym16111533.

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This study introduces the notions of BiHom-Poisson conformal algebra, BiHom-pre-Poisson conformal algebra, and their related structures. We show that many new BiHom-Poisson conformal algebras can be constructed from a BiHom-Poisson conformal algebra. In particular, the direct product of two BiHom-Poisson conformal algebras is also a BiHom-Poisson conformal algebra. We further describe the conformal bimodule and representation theory of the BiHom-Poisson conformal algebra. In addition, we define BiHom-pre-Poisson conformal algebra as the combination of BiHom-pre-Lie conformal algebra and BiHom-

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44

Minaiev, P. Ye, O. O. Pypka, and I. V. Shyshenko. "On Poisson (2-3)-algebras which are finite-dimensional over the center." Researches in Mathematics 32, no. 1 (2024): 118. http://dx.doi.org/10.15421/242411.

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One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous generalizations and modifications in group theory. At the same time, similar investigations were conducted in other algebraic structures, namely in modules, linear groups, topological groups, $n$-groups, associative algebras, Lie algebras, Lie $n$-algebras, Lie rings, Leibniz algebras. In 2021, L.A. Kurdachenko, O.O. Pypka and I.Ya. Subbotin proved an analogue of Sc

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45

Tong, Jie, and Quanqin Jin. "Non-commutative Poisson Algebra Structures on the Lie Algebra $so_n\widetilde{({\Bbb C}_Q)}$." Algebra Colloquium 14, no. 03 (2007): 521–36. http://dx.doi.org/10.1142/s100538670700048x.

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Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on [Formula: see text] are determined.

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46

Fernández, David, and Estanislao Herscovich. "Cyclic $A_\infty$-algebras and double Poisson algebras." Journal of Noncommutative Geometry 15, no. 1 (2021): 241–78. http://dx.doi.org/10.4171/jncg/412.

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47

Remm, Elisabeth. "Weakly associative algebras, Poisson algebras and deformation quantization." Communications in Algebra 49, no. 9 (2021): 3881–904. http://dx.doi.org/10.1080/00927872.2021.1909058.

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48

Pozhidaev, A. P. "Simple Poisson–Farkas Algebras and Ternary Filippov Algebras." Siberian Mathematical Journal 58, no. 6 (2017): 1071–77. http://dx.doi.org/10.1134/s0037446617060167.

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49

Xu, Ping. "Gerstenhaber Algebras and BV-Algebras in Poisson Geometry." Communications in Mathematical Physics 200, no. 3 (1999): 545–60. http://dx.doi.org/10.1007/s002200050540.

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50

Kaygorodov, Ivan. "Algebras of Jordan brackets and generalized Poisson algebras." Linear and Multilinear Algebra 65, no. 6 (2016): 1142–57. http://dx.doi.org/10.1080/03081087.2016.1229257.

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