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

Authors: Shlomo Gelaki and Edward S. Letzter
Journal: Proc. Amer. Math. Soc. 131 (2003), 2673-2679
MSC (2000): Primary 16W30; Secondary 16R20, 16W55
Published electronically: February 20, 2003
MathSciNet review: 1974322
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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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Additional Information

Shlomo Gelaki
Affiliation: Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

Edward S. Letzter
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Received by editor(s): December 5, 2001
Received by editor(s) in revised form: April 5, 2002
Published electronically: February 20, 2003
Additional Notes: The first author’s research was supported by the Technion V.P.R. Fund–Loewengart Research Fund, and by the Fund for the Promotion of Research at the Technion. The second author’s research was supported in part by NSF grant DMS-9970413. This research was begun during the second author’s visit to the Technion in August 2001, and he is grateful to the Technion for its hospitality.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2003 American Mathematical Society

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