Coideal subalgebras in hopf algebras: freeness, integrals, smash products
Coideal subalgebras in hopf algebras: freeness, integrals, smash products
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hopf 代数中的共理想子代数：自由度、积分、粉碎积
DOI：
10.1080/00927879308824572
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发表时间：
1993
影响因子：
0.7
通讯作者：
M. Koppinen
中科院分区：
文献类型：
--
作者：
M. Koppinen
A.Masuoka和Y.Doi给出了有限维Hopf代数A在右余理想子代数B上作为左模和右模自由的几个充要条件。我们得到了进一步的等价条件：例如B是A的左模和右模的直和，或者B包含某种称为积分的元素，或者Smash积#(A，B)和#op(A，B)以某种方式分解为卷积代数。我们还研究了当B的半单蕴含它的可分性时。
A. Masuoka and Y. Doi have given several necessary and sufficient conditions for a finite-dimensional Hopf algebra A to be free as a left and a right module over a right coideal subalgebra B. We derive further equivalent conditions: for example that B is a direct summand of A both as a left and a right B-module, or that B contains certain kind of elements called integrals, or that the smash products #(A,B) and #op (A,B) decompose as convolution algebras in a certain way. We study also when semisimplicity of B implies its separability.