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Post Closed as "no longer relevant" by Todd Trimble, Dan Petersen, Qiaochu Yuan, Scott Morrison♦
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Dimension of a Hopf algebra==sum algebra == sum of squares of its simple module??modules? |
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when I read an article,I find it seems there is a conclusion like the followings. $H$ is an Hopf algebra(or an abstract group). Then $dimH=\sum_{V:simple ~module ~of ~H}(dimV)^2$. who can tell me where I can find this content?Thank you very much. oh...It seems $H$ need to be semisimple! Oh...I think I already understand this.~When $H$ is a semisimple algebra.The above conclusion is right.For any Hopf algebra,maybe it's wrong. So please vote to close.Thanks everyone! |
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