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
Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibona...Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib Vecwz2 as fusion categories, where Fib is a Fibonacci category and Vecwz2 is a rank 2 pointed fusion category.展开更多
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 the Fundamental Research Funds for the Central Universities(Grant No.KYZ201564)the Natural Science Foundation of China(Grant Nos.11571173,11201231)the Qing Lan Project
文摘Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K（C） of C; that is, we prove that K（C） = Fib Z[Z2], where Fib is the Fibonacci fusion ring and Z[Z2] is the group ring on Z2. In particular, if C is braided, then it is equivalent to Fib Vecwz2 as fusion categories, where Fib is a Fibonacci category and Vecwz2 is a rank 2 pointed fusion category.
