Fullness of connes spectra and the connes hopf kernel |
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Authors: | James Osterburg Xue Yao |
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Institution: | Department of Mathematical Sciences , University of Cincinnati , Cincinnati, 45221-0025, Ohis E-mail: james.osterburg@uc.edu |
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Abstract: | Let H be a finite dimensional, semisimple Hopf algebra over a field K and let A be an H- module algebra. Assume K is a splitting field for H and that H is strongly semiprime. If A is H- semiprime, we show the Connes spectrum of H acting on A consists of all of the irreducible representations of H is equivalent to every nonzero annihilator ideal of the smash product meets A nontrivially. If H is also cocommutative, we let I′ be the intersection of the annihilators of the modules in the Connes spectrum. We find some of the information encoded in the Hopf kernel of the natural map from H to H/I′. |
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Keywords: | Primary 16W30 Secondary 16W20 |
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