Results 21 to 30 of about 85,344 (218)
Hall algebras as Poisson algebras [PDF]
SCIENTIA SINICA Mathematica, 2018 Motivated by Joyces work on motivic Hall algebras, we observe that for an algebra $\Lambda$ with Hall polynomials,the Hall algebra $\mathcal{H}(\Lambda)$ of $\Lambda$ admits a natural structure of Poisson algebra. For a given antisymmetric bilinear form over its Grothendieck group $\go(\Lambda)$satisfying certain condition, there is a homomorphism of ...
Fu Changjian, Peng Lian'gang
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Transactions of the American Mathematical Society, 2007 We study Poisson algebras satisfying polynomial identities. In particular, such algebras satisfy “customary” identities (Farkas, 1998, 1999) Our main result is that the growth of the corresponding codimensions of a Poisson algebra with a nontrivial identity is exponential, with an integer exponent.
Mishchenko, S. P. +2 more
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Transposed Poisson superalgebra [PDF]
Proceedings of the Estonian Academy of SciencesIn this paper, we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra.
Viktor Abramov, Olga Liivapuu
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Poisson catenarity in Poisson nilpotent algebras
Journal of Algebra, 2022 We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Poisson prime ideals have the same length.
Goodearl, K. R., Launois, S.
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On double Poisson structures on commutative algebras [PDF]
, 2016 Double Poisson structures (a la Van den Bergh) on commutative algebras are studied; the main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one.
Powell, Geoffrey
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Normalization of a Poisson algebra is Poisson [PDF]
Proceedings of the Steklov Institute of Mathematics, 2009 We prove that the integral closure of a Poisson algebra $A$ over a field of characteristic 0 is again a Poisson algebra.
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Quasilocal angular momentum of gravitational fields in (2+2) formalism
EPJ Web of Conferences, 2018 Recently the Poisson algebra of a quasilocal angular momentum of gravitational fields L(ξ) in (2+2) formalism of Einstein’s theory was studied in detail [1].
Oh Seung Hun, Yoon Jong Hyuk
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On the Yang–Baxter Poisson algebra in non-ultralocal integrable systems
Nuclear Physics B, 2018 A common approach to the quantization of integrable models starts with the formal substitution of the Yang–Baxter Poisson algebra with its quantum version.
Vladimir V. Bazhanov +2 more
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On W1+∞ 3-algebra and integrable system
Nuclear Physics B, 2015 We construct the W1+∞ 3-algebra and investigate its connection with the integrable systems. Since the W1+∞ 3-algebra with a fixed generator W00 in the operator Nambu 3-bracket recovers the W1+∞ algebra, it is intrinsically related to the KP hierarchy ...
Min-Ru Chen +4 more
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Poisson Algebra of Differential Forms [PDF]
International Journal of Modern Physics A, 1997 We give a natural definition of a Poisson differential algebra. Consistency conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on the differential calculus in a simple canonical form by a coordinate trans-formation.
Chu, Chong-Sun, Ho, Pei-Ming
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