On the combinatorial rank of a graded braided bialgebra |
| |
Authors: | Alessandro Ardizzoni |
| |
Institution: | University of Ferrara, Department of Mathematics, Via Machiavelli 35, Ferrara, I-44121, Italy |
| |
Abstract: | Let B be a graded braided bialgebra. Let S(B) denote the algebra obtained dividing out B by the two sided ideal generated by homogeneous primitive elements in B of degree at least two. We prove that S(B) is indeed a graded braided bialgebra quotient of B. It is then natural to compute S(S(B)), S(S(S(B))) and so on. This process yields a direct system whose direct limit comes out to be a graded braided bialgebra which is strongly N-graded as a coalgebra. Following V.K. Kharchenko, if the direct system is stationary exactly after n steps, we say that B has combinatorial rank n and we write κ(B)=n. We investigate conditions guaranteeing that κ(B) is finite. In particular, we focus on the case when B is the braided tensor algebra T(V,c) associated to a braided vector space (V,c), providing meaningful examples such that κ(T(V,c))≤1. |
| |
Keywords: | Primary 16W30 Secondary 16W50 |
本文献已被 ScienceDirect 等数据库收录! |
|