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
For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson...For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.展开更多
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.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11771085）.
文摘For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.
