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An affine PI Hopf algebra not finite over a normal commutative Hopf subalgebra
Author(s):
Shlomo
Gelaki;
Edward
S.
Letzter
Journal:
Proc. Amer. Math. Soc.
131
(2003),
2673-2679.
MSC (2000):
Primary 16W30;
Secondary 16R20, 16W55
Posted:
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  , 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:
10.1090/S0002-9939-03-06815-1
PII:
S 0002-9939(03)06815-1
Received by editor(s):
December 5, 2001
Received by editor(s) in revised form:
April 5, 2002
Posted:
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 of article:
Copyright
2003,
American Mathematical Society
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