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Frontiers of Mathematics in China, ISSN 1673-3452, 8/2018, Volume 13, Issue 4, pp. 999 - 1011
For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping... 
16E65 | 17B63 | deformation quantization | Mathematics, general | Mathematics | 16S80 | Poisson enveloping algebra | quantized universal enveloping algebra | MATHEMATICS | MANIFOLDS | COHOMOLOGY | Algebra | Deformation | Poisson distribution | Mathematical analysis
Journal Article
Journal of Algebra, ISSN 0021-8693, 03/2015, Volume 426, pp. 92 - 136
For a Poisson algebra A, by exploring its relation with Lie–Rinehart algebras, we prove a Poincaré–Birkhoff–Witt theorem for its universal enveloping algebra... 
Universal enveloping algebras | Poisson Hopf algebras | Hopf algebras | Lie–Rinehart algebras | Lie-Rinehart algebras | MATHEMATICS | DIMENSION | Algebra
Journal Article
Communications in Algebra, ISSN 0092-7872, 11/2018, Volume 46, Issue 11, pp. 4891 - 4904
It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are... 
Poisson enveloping algebra | Double Ore extension | double Poisson-Ore extension | MATHEMATICS | BIRKHOFF-WITT THEOREM | Algebra
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 1/2013, Volume 29, Issue 1, pp. 105 - 118
We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative... 
Poisson module | 17B63 | 16S40 | Mathematics, general | Mathematics | Non-commutative Poisson algebra | Poisson enveloping algebra | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | LEIBNIZ PAIRS | POISSON ALGEBRAS | Algebra | Studies | Poisson distribution | Mathematical analysis | Equivalence | Categories | Modules
Journal Article
Journal of Algebra, ISSN 0021-8693, 09/2017, Volume 485, pp. 166 - 198
Poisson algebras are, just like Lie algebras, particular cases of Lie–Rinehart algebras. The latter were introduced by Rinehart in his seminal 1963 paper,... 
Poisson structures | Singularities | Enveloping algebras | MATHEMATICS | Algebra | Mathematics | Rings and Algebras
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2015, Volume 143, Issue 11, pp. 4633 - 4645
We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra.... 
Ore extension | Universal enveloping algebra | Poisson algebra | Mathematics - Rings and Algebras
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2016, Volume 59, Issue 5, pp. 849 - 860
Journal Article
Communications in Algebra, ISSN 0092-7872, 06/2018, Volume 46, Issue 6, pp. 2714 - 2729
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson... 
differential graded Poisson algebras | Differential graded Hopf algebras | differential graded Poisson Hopf algebras | universal enveloping algebras | MATHEMATICS | Algebra
Journal Article
Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 11/2019, Volume 42, Issue 6, pp. 3343 - 3377
For any differential graded (DG for short) Poisson algebra A given by generators and relations, we give a “formula” for computing the universal enveloping... 
Universal enveloping algebras | 16S10 | 17B35 | 17B63 | Simple differential graded Poisson module | Mathematics, general | Differential graded Poisson algebras | Mathematics | Applications of Mathematics | PBW-basis | 16E45 | MATHEMATICS | Polynomials | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 03/2012, Volume 354, Issue 1, pp. 77 - 94
Let k be an arbitrary field of characteristic 0. It is shown that for any n⩾1 the universal enveloping algebras of the Poisson symplectic algebra Pn(k) and the... 
Poisson algebras | Universal enveloping algebras | Derivations | Left dependence | Automorphisms | Secondary | Primary | LIE-ALGEBRAS | POLYNOMIALS | MATHEMATICS | RINGS | JACOBIAN CONJECTURE | WEYL ALGEBRA | ENDOMORPHISMS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 07/2010, Volume 43, Issue 29, p. 293001
This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations... 
GAUGE-THEORIES | PHYSICS, MULTIDISCIPLINARY | UNITARY GROUP | ENVELOPING-ALGEBRAS | LEIBNIZ ALGEBRAS | DEFORMATION QUANTIZATION | SCHOUTEN-NIJENHUIS BRACKET | GRADED LIE-ALGEBRAS | NAMBU-MECHANICS | PHYSICS, MATHEMATICAL | STRING THEORY | GENERALIZED POISSON
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 7/2013, Volume 54, Issue 4, pp. 759 - 768
Under study are the centralizers of 3-dimensional simple Lie subalgebras in the universal enveloping algebra of a 7-dimensional simple Malcev algebra. We find... 
alternative algebra | algebra of octonions | Mathematics, general | Poisson bracket | Mathematics | universal enveloping algebra | Lie algebra | Malcev algebra | MATHEMATICS | Public contracts | Algebra
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2017, Volume 488, pp. 244 - 281
Journal Article
Journal of Algebra, ISSN 0021-8693, 05/2017, Volume 477, pp. 95 - 146
Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We provide necessary and also some sufficient conditions... 
Semi-invariants | Polynomiality | Poisson center | Dixmier's fourth problem | Enveloping algebra | QUOTIENT DIVISION RING | INVARIANTS | THEOREM | BIPARABOLIC SEAWEED ALGEBRAS | MATHEMATICS | DIMENSION | GELFAND-KIRILLOV CONJECTURE | COMMUTATIVE SUBALGEBRAS | INDEX | Polynomiality Enveloping algebra | ENVELOPING ALGEBRA | Algebra | Mathematics - Representation Theory
Journal Article
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9939, 11/2015, Volume 143, Issue 11, pp. 4633 - 4645
We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra.... 
MATHEMATICS | Ore extension | MATHEMATICS, APPLIED | Poisson algebra | universal enveloping algebra
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 9/2017, Volume 107, Issue 9, pp. 1715 - 1740
Journal Article
International Journal of Theoretical Physics, ISSN 0020-7748, 2/2008, Volume 47, Issue 2, pp. 311 - 332
We describe enveloping algebras of finite-dimensional Lie algebras which are formal in the sense that their Hochschild complex as a differential graded Lie... 
Quantum Physics | Physics, general | Mathematical and Computational Physics | Physics | Elementary Particles, Quantum Field Theory | LIE-ALGEBRAS | POISSON MANIFOLDS | COHOMOLOGY | PHYSICS, MULTIDISCIPLINARY | QUANTIZATION | STAR-PRODUCT
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 12/2016, Volume 15, Issue 10
Let k be an arbitrary field of characteristic 0. We prove that the group of automorphisms of a free Poisson field P(x, y) in two variables x, y over k is... 
Poisson algebras | left dependence | universal enveloping algebras | automorphisms | MATHEMATICS | MATHEMATICS, APPLIED | ENVELOPING-ALGEBRAS | RINGS | FREE ASSOCIATIVE ALGEBRA
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 03/2018, Volume 17, Issue 3
We prove that when Kontsevich's deformation quantization is applied on weight homo-geneous Poisson structures, the operators in the *-product formula are... 
Deformation quantization | semisimple Lie algebras | transverse Poisson structures | W -algebras | Slodowy slice | MATHEMATICS, APPLIED | COISOTROPIC SUBMANIFOLDS | REPRESENTATIONS | SLODOWY SLICES | MATHEMATICS | W-algebras | SYMMETRICAL SPACES | ENVELOPING-ALGEBRAS | INVARIANT DIFFERENTIAL-OPERATORS | QUANTIZATION
Journal Article
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