The cohomology of certain Hopf algebras associated with -groups

Author:
Justin M. Mauger

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3301-3323

MSC (2000):
Primary 16E40; Secondary 16S37, 16S30

DOI:
https://doi.org/10.1090/S0002-9947-03-03381-6

Published electronically:
November 12, 2003

MathSciNet review:
2052951

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Abstract: We study the cohomology of a locally finite, connected, cocommutative Hopf algebra over . Specifically, we are interested in those algebras for which is generated as an algebra by and . We shall call such algebras *semi-Koszul*. Given a central extension of Hopf algebras with monogenic and semi-Koszul, we use the Cartan-Eilenberg spectral sequence and algebraic Steenrod operations to determine conditions for to be semi-Koszul. Special attention is given to the case in which is the restricted universal enveloping algebra of the Lie algebra obtained from the mod- lower central series of a -group. We show that the algebras arising in this way from extensions by of an abelian -group are semi-Koszul. Explicit calculations are carried out for algebras arising from rank 2 -groups, and it is shown that these are all semi-Koszul for .

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Additional Information

**Justin M. Mauger**

Affiliation:
Department of Mathematics, Whittier College, Whittier, California 90608

Address at time of publication:
Department of Mathematics and Computer Science, California State University, Channel Islands, Camarillo, California 93012

Email:
jmauger@whittier.edu, justin.mauger@csuci.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03381-6

Keywords:
Koszul algebras,
cohomology of algebras,
Hopf algebras

Received by editor(s):
April 30, 2002

Received by editor(s) in revised form:
April 2, 2003

Published electronically:
November 12, 2003

Article copyright:
© Copyright 2003
American Mathematical Society