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PBW-Bases of Coideal Subalgebras and a Freeness Theorem

V. K. Kharchenko
Transactions of the American Mathematical Society
Vol. 360, No. 10 (Oct., 2008), pp. 5121-5143
Stable URL: http://www.jstor.org/stable/20161460
Page Count: 23
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PBW-Bases of Coideal Subalgebras and a Freeness Theorem
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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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