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

DOI:
https://doi.org/10.1090/S0002-9939-03-06815-1

Published electronically:
February 20, 2003

MathSciNet review:
1974322

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Abstract | References | Similar Articles | Additional Information

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 , 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

Email:
gelaki@math.technion.ac.il

**Edward S. Letzter**

Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122

Email:
letzter@math.temple.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-06815-1

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