On the adjoint representation of a hopf algebra
2020 ◽
Vol 63
(4)
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pp. 1092-1099
Keyword(s):
AbstractWe consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{{\textrm ad\,fin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as module over a cocommutative Hopf subalgebra), we show that $H_{{\textrm ad\,fin}}$ is a Hopf subalgebra of $H$. This is a consequence of the fact, proved here, that locally finite parts yield a tensor functor on the module category of any virtually pointed Hopf algebra. For general Hopf algebras, $H_{{\textrm ad\,fin}}$ is shown to be a left coideal subalgebra. We also prove a version of Dietzmann's Lemma from group theory for Hopf algebras.
2008 ◽
Vol 2
(1)
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pp. 1-40
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2016 ◽
Vol 15
(04)
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pp. 1650059
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Keyword(s):
2014 ◽
Vol 23
(07)
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pp. 1460001
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2010 ◽
Vol 09
(01)
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pp. 11-15
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Keyword(s):
1982 ◽
Vol 91
(2)
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pp. 215-224
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2014 ◽
Vol 14
(02)
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pp. 1550021