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Transactions of the American Mathematical Society

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PBW-bases of coideal subalgebras and a freeness theorem

Author: V. K. Kharchenko
Journal: Trans. Amer. Math. Soc. 360 (2008), 5121-5143
MSC (2000): Primary 16W30, 16W35; Secondary 17B37.
Published electronically: April 10, 2008
MathSciNet review: 2415067
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Abstract: Let $ H$ be a character Hopf algebra. Every right coideal subalgebra U that contains the coradical has a PBW-basis which can be extended up to a PBW-basis of $ H.$ If additionally U is a bosonization of an invariant with respect to the left adjoint action subalgebra, then $ H$ is a free left (and right) U-module with a free PBW-basis over U. These results remain valid if $ H$ is a braided Hopf algebra generated by a categorically ordered subset of primitive elements. If the ground field is algebraically closed, the results are still true provided that $ H$ is a pointed Hopf algebra with commutative coradical and is generated over the coradical by a direct sum of finite-dimensional Yetter-Drinfeld submodules of skew primitive elements.

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V. K. Kharchenko
Affiliation: FES-Cuautitlan, Universidad Nacional Autónoma de México, Centro de Investigaciones Teóricas, Primero de Mayo s/n, Campo 1, CIT, Cuautitlan Izcalli, Edstado de México, 54768, Mexico

Keywords: Hopf algebra, coideal subalgebra, PBW-basis.
Received by editor(s): February 8, 2006
Published electronically: April 10, 2008
Additional Notes: The author was supported by PAPIIT IN 108306-3, UNAM, México.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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