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ISSN 1088-6850(e) ISSN 0002-9947(p)

PBW-bases of coideal subalgebras and a freeness theorem

Author(s): V. K. Kharchenko
Journal: Trans. Amer. Math. Soc. 360 (2008), 5121-5143.
MSC (2000): Primary 16W30, 16W35; Secondary 17B37.
Posted: April 10, 2008
MathSciNet review: 2415067
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Abstract: Let 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 If additionally U is a bosonization of an invariant with respect to the left adjoint action subalgebra, then is a free left (and right) U-module with a free PBW-basis over U. These results remain valid if 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 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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