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Gocommutative Hopf Algebras

Published online by Cambridge University Press:  20 November 2018

Richard G. Larson
Richard G. Larson*
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts
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A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that

1

and

2

The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ). If A is also an algebra with unit and δ and ∊ are algebra homomorphisms, A is a Hopf algebra.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 350 - 360
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vol. 1 (Providence, 1956).Google Scholar
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3. Jacobson, N., Structure of rings (Providence, 1956).Google Scholar
4. MacLane, S., Categorical algebra, Bull. Amer. Math. Soc., 71 (1965), 40–106.Google Scholar
5. Milnor, J. W. and Moore, J. C., On the structure of Hopf algebras, Ann. Math., (2) 81 (1965), 211–264.Google Scholar