PBW-bases of coideal subalgebras and a freeness theorem

Kharchenko, V.

doi:10.1090/S0002-9947-08-04483-8

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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