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A Note on the Representation Type of Pointed Irreducible Coalgebras and Unipotent Algebras

Published online by Cambridge University Press:  20 November 2018

David Trushin
David Trushin*
Affiliation:
The Ohio State University, Columbus, Ohio
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Abstract

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In this paper the representation type of the class of pointed irreducible coalgebras is studied. We refer the reader to [4] for the basic definitions. A coalgebra is of bounded representation type if there is a bound on the dimension of finite dimensional indecomposable comodules. In Section 1, we show that the representation type is dependent upon the size of the space of primitives. Indeed, a pointed irreducible coalgebra is of bounded type if and only if it is finite dimensional and the space of primitives is onedimensional, i.e. if and only if it is a coalgebra spanned by a finite sequence of divided powers.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 220 - 223
Copyright
Copyright © Canadian Mathematical Society 1977

Footnotes

Part of this research is contained in the author's doctoral dissertation.

References

1. Allen, H. P., Invariant radical splittings: a Hopf approach, Journal of Pure and Applied Algebra 3 (1973), 1–19.Google Scholar
2. Curtis, Charles W. and Reiner, Irving, Representation theory of finite groups and associative algebras (Interscience Publishers, New York, 1966).Google Scholar
3. Pollack, Richard D., Restricted Lie algebras of bounded type, Ph.D. Dissertation, Yale University, 1967.Google Scholar
4. Sweedler, Moss E., Hopf algebras (W. A. Benjamin, Inc., New York, 1969).Google Scholar
5. Trushin, David S., Coinduced comodules and applications to the representation theory of coalgebras, Ph.D. Dissertation, The Ohio State University, Columbus, Ohio, 1975.Google Scholar