Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures...Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.展开更多
Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on...Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.展开更多
We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We...We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.展开更多
For a Poisson algebra,we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived functor.We show that the(generalized)deformation quantization is equivalent to the formal...For a Poisson algebra,we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived functor.We show that the(generalized)deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild conditions.Finally we construct a long exact sequence,and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups.展开更多
The graded modules for the Poisson algebras K are inverstigated and their compositionfactors are determined. Also, a revision on the realizations of the irreducible PTG H(n,m)-modules V(n, m) due to Shen is made.
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the...Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.展开更多
The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.展开更多
We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of c...We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Poisson color algebras A is of the form A = U +Σα Iα with U a subspace of a maximal abelian subalgebra H and any Iα , a well described ideal of A, satisfying [Iα,Iβ]+ IαIβ= 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.展开更多
In this paper, we study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the i...In this paper, we study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the induction on the length. The calculation methods provided in this paper can also solve truncated polynomials algebra in a few variables.展开更多
We provide a detailed description of inner and outer Poisson structures for the trivial extension A D(A),where A is a hereditary algebra of Dynkin type An and D(A)=Homk(A,K).
The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure...The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.展开更多
The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the speci...The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.展开更多
基金supported by NSF of China(11071187)Innovation Program of Shanghai Municipal Education Commission(09YZ336)
文摘Non-commutative Poisson algebras are the algebras having both an associa- tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln（Cq^-） are determined.
基金This work is partially supported by NNSF of China(10671124)the Specialized Research Fund for the Doctoral Program of Higher Education(20040247024).
文摘Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l（^～CQ） are determined.
基金Acknowledgements Part of the work was done during the author＇s visit to SCMS （Shanghai Center for Mathematical Sciences）, and the author would like to thank for the hospitality. The author also thank the referees for their careful reading, helpful suggestions and comments. This work was supported by the National Natural Science Foundation of China （Grant No. 11301180）.
文摘We compute explicitly the modular derivations for Poisson-Ore extensions and tensor products of Poisson algebras.
基金supported by National Natural Science Foundation of China(Grant Nos.11571316 and 11001245)Natural Science Foundation of Zhejiang Province(Grant No.LY16A010003)
文摘We introduce the notions of differential graded(DG) Poisson algebra and DG Poisson module. Let A be any DG Poisson algebra. We construct the universal enveloping algebra of A explicitly, which is denoted by A^(ue). We show that A^(ue) has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over A is isomorphic to the category of DG modules over A^(ue). Furthermore, we prove that the notion of universal enveloping algebra A^(ue) is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
基金supported by National Natural Science Foundation of China(Grant Nos.11401001,11871071,11431010 and 11571329)。
文摘For a Poisson algebra,we prove that the Poisson cohomology theory introduced by Flato et al.(1995)is given by a certain derived functor.We show that the(generalized)deformation quantization is equivalent to the formal deformation for Poisson algebras under certain mild conditions.Finally we construct a long exact sequence,and use it to calculate the Poisson cohomology groups via the Yoneda-extension groups of certain quasi-Poisson modules and the Lie algebra cohomology groups.
文摘The graded modules for the Poisson algebras K are inverstigated and their compositionfactors are determined. Also, a revision on the realizations of the irreducible PTG H(n,m)-modules V(n, m) due to Shen is made.
基金This work is supported by the National Natural Science Foundation of China (Grant No.10171064)two grants 'Excellent Young Teacher Program' and 'Trans-Century Training Programme Foundation for the Talents' from Ministry of Education of China.
文摘Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
基金Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10471145 and 10372053） and the Natural Science Foundation of Henan Provincial Government of China （Grant Nos 0311011400 and 0511022200）.
文摘The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
基金Supported by the National Natural Science Foundation of China(Grant No.11761017)the Youth Project for Natural Science Foundation of Guizhou Provincial Department of Education(Grant No.KY[2018]155)
文摘We introduce the class of split regular Hom-Poisson color algebras as the natural generalization of split regular Hom-Poisson algebras and the one of split regular Hom-Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Poisson color algebras A is of the form A = U +Σα Iα with U a subspace of a maximal abelian subalgebra H and any Iα , a well described ideal of A, satisfying [Iα,Iβ]+ IαIβ= 0 if [α]≠[β]. Under certain conditions, in the case of A being of maximal length, the simplicity of the algebra is characterized.
文摘In this paper, we study the twisted Poisson homology of truncated polynomials algebra A in four variables, and we calculate exactly the dimension of i-th (i = 1, 2, 3, 4) twisted Poisson homology group over A by the induction on the length. The calculation methods provided in this paper can also solve truncated polynomials algebra in a few variables.
文摘We provide a detailed description of inner and outer Poisson structures for the trivial extension A D(A),where A is a hereditary algebra of Dynkin type An and D(A)=Homk(A,K).
基金supported by the National Natural Science Foundation of China(10772025,10932002,10972031)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics
文摘The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.
文摘The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.
