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A Characterization of Group Rings as a Special Class of Hopf Algebras

Published online by Cambridge University Press:  20 November 2018

Shuichi Takahashi
Shuichi Takahashi*
Affiliation:
Université de Montréal
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By a group ring we mean in this paper a ring defined by a finite group G and an integral domain K:

such that A contains G and is freely generated by G over K, so that

The ring A = KG has a co-multiplication

defined by

so that A is a Hopf algebra.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 4 , June 1965 , pp. 465 - 475
Copyright
Copyright © Canadian Mathematical Society 1965

References

1) In particular J. L. Kelley, Duality for compact groups, Proc. N. A. S. 49 (1963) pp. 457-458.

*) The author would like to thank Professor Geoffrey Fox and the referee for their valuable suggestions.

2) We follow the presentation of S. MacLane, Homology, 1963, pp. 197-198.

3) Always commutative with the identity 1.