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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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PBW-bases of coideal subalgebras and a freeness theorem
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by V. K. Kharchenko PDF
Trans. Amer. Math. Soc. 360 (2008), 5121-5143 Request permission

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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Additional Information
  • 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
  • Email: vlad@servidor.unam.mx
  • 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.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5121-5143
  • MSC (2000): Primary 16W30, 16W35; Secondary 17B37
  • DOI: https://doi.org/10.1090/S0002-9947-08-04483-8
  • MathSciNet review: 2415067