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.References
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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
- MR Author ID: 113075
- Email: letzter@math.temple.edu
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1974322