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Journal articles on the topic 'Poisson algebras'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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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 (September 27, 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

Changjian, Fu, and Peng Lian'gang. "Hall algebras as Poisson algebras." SCIENTIA SINICA Mathematica 48, no. 11 (August 30, 2018): 1673. http://dx.doi.org/10.1360/n012017-00268.

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3

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

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4

Ait Ben Haddou, Malika, Saïd Benayadi, and Said Boulmane. "Malcev–Poisson–Jordan algebras." Journal of Algebra and Its Applications 15, no. 09 (August 22, 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-structures on some interesting classes of Malcev algebras. Further, we introduce the concept of pseudo-Euclidean MPJ-algebras (PEMPJ-algebras) and we show how one can construct new interesting quadratic Lie algebras and pseudo-Euclidean Malcev (non-Lie) algebras from PEMPJ-algebras. Finally, we give inductive descriptions of nilpotent PEMPJ-algebras.

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5

LI, HAISHENG. "VERTEX ALGEBRAS AND VERTEX POISSON ALGEBRAS." Communications in Contemporary Mathematics 06, no. 01 (February 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 filtrations are given. To each ℕ-graded vertex algebra V=∐n∈ℕV(n) with [Formula: see text], a canonical (good) filtration is associated and certain results about generating subspaces of certain types of V are also obtained. Furthermore, a notion of formal deformation of a vertex (Poisson) algebra is formulated and a formal deformation of vertex Poisson algebras associated with vertex Lie algebras is constructed.

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6

Safronov, Pavel. "Braces and Poisson additivity." Compositio Mathematica 154, no. 8 (July 18, 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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7

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

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8

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

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9

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

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10

Van den Bergh, Michel. "Double Poisson algebras." Transactions of the American Mathematical Society 360, no. 11 (June 5, 2008): 5711–69. http://dx.doi.org/10.1090/s0002-9947-08-04518-2.

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11

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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12

Bao, Yan-Hong, Yu Ye, and James Zhang. "Restricted Poisson algebras." Pacific Journal of Mathematics 289, no. 1 (May 12, 2017): 1–34. http://dx.doi.org/10.2140/pjm.2017.289.1.

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13

Luo, Juan, Shengqiang Wang, and Quanshui Wu. "Frobenius Poisson algebras." Frontiers of Mathematics in China 14, no. 2 (March 21, 2019): 395–420. http://dx.doi.org/10.1007/s11464-019-0756-x.

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14

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

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15

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

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16

Chtioui, T., S. Mabrouk, and A. Makhlouf. "Hom–Jordan–Malcev–Poisson algebras." Ukrains’kyi Matematychnyi Zhurnal 74, no. 11 (December 26, 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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17

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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18

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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19

Kolesnikov, P. S. "Universal enveloping Poisson conformal algebras." International Journal of Algebra and Computation 30, no. 05 (March 20, 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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20

OKASSA, EUGÈNE. "ON LIE–RINEHART–JACOBI ALGEBRAS." Journal of Algebra and Its Applications 07, no. 06 (December 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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21

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

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22

Ratseev, S. M. "COMMUTATIVE LEIBNIZ-POISSON ALGEBRAS OF POLYNOMIAL GROWTH." Vestnik of Samara University. Natural Science Series 18, no. 3.1 (June 7, 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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23

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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24

Ratseev, S. M. "On minimal Poisson algebras." Russian Mathematics 59, no. 11 (October 15, 2015): 54–61. http://dx.doi.org/10.3103/s1066369x15110067.

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25

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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26

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

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27

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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28

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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29

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

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30

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

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31

Yang, Yan Hong, Yuan Yao, and Yu Ye. "(Quasi-)Poisson enveloping algebras." Acta Mathematica Sinica, English Series 29, no. 1 (September 20, 2012): 105–18. http://dx.doi.org/10.1007/s10114-012-1041-z.

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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 (October 1, 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 (August 2004): 363–95. http://dx.doi.org/10.1016/j.aim.2003.08.007.

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35

Zhu, Can, Fred Van Oystaeyen, and Yinhuo Zhang. "On (co)homology of Frobenius Poisson algebras." Journal of K-Theory 14, no. 2 (September 5, 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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36

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 (March 28, 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 Balinsky-Novikov algebras are described in depth.

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37

Su, Yucai. "Poisson Brackets and Structure of Nongraded Hamiltonian Lie Algebras Related to Locally-Finite Derivations." Canadian Journal of Mathematics 55, no. 4 (August 1, 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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38

Fehlberg Júnior, R., and I. Kaygorodov. "On the Kantor product, II." Carpathian Mathematical Publications 14, no. 2 (December 30, 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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39

NGAKEU, FERDINAND. "GRADED POISSON STRUCTURES AND SCHOUTEN–NIJENHUIS BRACKET ON ALMOST COMMUTATIVE ALGEBRAS." International Journal of Geometric Methods in Modern Physics 09, no. 05 (July 3, 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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40

Fernández, David, and Estanislao Herscovich. "Cyclic $A_\infty$-algebras and double Poisson algebras." Journal of Noncommutative Geometry 15, no. 1 (April 21, 2021): 241–78. http://dx.doi.org/10.4171/jncg/412.

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41

Remm, Elisabeth. "Weakly associative algebras, Poisson algebras and deformation quantization." Communications in Algebra 49, no. 9 (May 10, 2021): 3881–904. http://dx.doi.org/10.1080/00927872.2021.1909058.

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42

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

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43

Xu, Ping. "Gerstenhaber Algebras and BV-Algebras in Poisson Geometry." Communications in Mathematical Physics 200, no. 3 (February 1, 1999): 545–60. http://dx.doi.org/10.1007/s002200050540.

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44

Kaygorodov, Ivan. "Algebras of Jordan brackets and generalized Poisson algebras." Linear and Multilinear Algebra 65, no. 6 (September 8, 2016): 1142–57. http://dx.doi.org/10.1080/03081087.2016.1229257.

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45

Zhelyabin, V. N., and A. S. Tikhov. "Novikov-Poisson algebras and associative commutative derivation algebras." Algebra and Logic 47, no. 2 (March 2008): 107–17. http://dx.doi.org/10.1007/s10469-008-9002-4.

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46

Goze, Michel, and Elisabeth Remm. "Poisson algebras in terms of non-associative algebras." Journal of Algebra 320, no. 1 (July 2008): 294–317. http://dx.doi.org/10.1016/j.jalgebra.2008.01.024.

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47

Kurdachenko, L. A., A. A. Pypka, and I. Ya Subbotin. "On extension of classical Baer results to Poisson algebras." Algebra and Discrete Mathematics 31, no. 1 (2021): 84–108. http://dx.doi.org/10.12958/adm1758.

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In this paper we prove that if P is a Poisson algebra and the n-th hypercenter (center) of P has a finite codimension, then P includes a finite-dimensional ideal K such that P/K is nilpotent (abelian). As a corollary, we show that if the nth hypercenter of a Poisson algebra P (over some specific field) has a finite codimension and P does not contain zero divisors, then P is an abelian algebra.

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48

Sánchez, J. M. "On Split Malcev Poisson Algebras." Siberian Mathematical Journal 62, no. 3 (May 2021): 511–20. http://dx.doi.org/10.1134/s0037446621030149.

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49

Omori, Hideki, Yoshiaki Maeda, and Akira Yoshioka. "Deformation quantization of Poisson algebras." Proceedings of the Japan Academy, Series A, Mathematical Sciences 68, no. 5 (1992): 97–100. http://dx.doi.org/10.3792/pjaa.68.97.

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50

Mroczyńska, Karolina, and Zygmunt Pogorzały. "Zero-relation quiver Poisson algebras." Colloquium Mathematicum 154, no. 2 (2018): 167–81. http://dx.doi.org/10.4064/cm7426-12-2017.

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