An affine PI Hopf algebra not finite over a normal commutative Hopf subalgebra

Gelaki, Shlomo; Letzter, Edward

doi:10.1090/S0002-9939-03-06815-1

An affine PI Hopf algebra not finite over a normal commutative Hopf subalgebra
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by Shlomo Gelaki and Edward S. Letzter PDF

Proc. Amer. Math. Soc. 131 (2003), 2673-2679 Request permission

Abstract:

In formulating a generalized framework to study certain noncommutative algebras naturally arising in representation theory, K. A. Brown asked if every finitely generated Hopf algebra satisfying a polynomial identity was finite over a normal commutative Hopf subalgebra. In this note we show that Radford’s biproduct, applied to the enveloping algebra of the Lie superalgebra $\operatorname {pl}(1,1)$, provides a noetherian prime counterexample.

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