This paper gives a sufficient and necessary condition for a bialgebra to be a Long bialgebra, and proves a braided product to be a Long bialgebra under some conditions. It also gives a direct sum decomposition of quan...This paper gives a sufficient and necessary condition for a bialgebra to be a Long bialgebra, and proves a braided product to be a Long bialgebra under some conditions. It also gives a direct sum decomposition of quantum Yang-Baxter modules over Long bialgebras.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National Natural Science Foundation of P.R.China No.10571153Post-Doctoral Program of P.R.China,No.2005037713+1 种基金Post-Doctoral Program of Jiangsu Province of China No.0203003403National Science Foundation of Jiangsu Province of China
文摘This paper gives a sufficient and necessary condition for a bialgebra to be a Long bialgebra, and proves a braided product to be a Long bialgebra under some conditions. It also gives a direct sum decomposition of quantum Yang-Baxter modules over Long bialgebras.
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.
