The monoidal center construction and bimodules

被引:48
作者
Schauenburg, P [1 ]
机构
[1] Univ Munich, Inst Math, D-80333 Munich, Germany
关键词
D O I
10.1016/S0022-4049(00)00040-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let E be a cocomplete monoidal category such that the tenser product in E preserves colimits in each argument. Let A be an algebra in E. We show (under some assumptions including "faithful flatness" of A) that the center of the monoidal category ((A)E(A), circle times (A)) of A-A-bimodules is equivalent to the center of E (hence in a sense trivial): L((A)E(A)) congruent to L(E) Assuming A to be a commutative algebra in the center L(E), we compute the center L(E(A)) of the category of right A-modules (considered as a subcategory of (A)E(A) using the structure of A is an element of L(E). We find L(E(A)) congruent to dys L(E)(A), the category of dyslectic right A-modules in the braided category L(E) (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:325 / 346
页数:22
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