Journal ArticleDOI
Freeness of hopf algebras over coideal subalgebras
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The notion of hopf algebras over coideal subalgeses was introduced in this article, where the authors show that hopf algebra can be viewed as a hopf subalgebra.Abstract:
(1992). Freeness of hopf algebras over coideal subalgebras. Communications in Algebra: Vol. 20, No. 5, pp. 1353-1373.read more
Citations
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Semisimple Hopf algebras of dimension 6, 8
TL;DR: In this paper, the isomorphic classes of 6 or 8 dimensional semisimple Hopf algebras over an algebraically closed field such that (dimA)1≠0.
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Projectivity and freeness over comodule algebras
TL;DR: In this paper it was shown that every Hopf algebra is projective or free as an A-module and A is either a quasi-Frobenius or a semisimple ring.
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On Semisimple Hopf Algebras of Dimension pq2
TL;DR: In this article, it was shown that if A is a semisimple Hopf algebra of dimension pq2 over an algebraically closed field k of characteristic zero, then under certain restrictions either A or A* must have a non-trivial central group-like element.
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Semisimple hopf algebras of dimension 2p
TL;DR: In this article, the isomorphic classes of 6 or 8 dimensional semisimple Hopf algebras over an algebraically closed field such that (dimA)1≠0.
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Projectivity and freeness over comodule algebras
TL;DR: In this paper it was shown that every weakly finite Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras.
References
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Book
Representation Theory of Finite Groups and Associative Algebras
Charles W. Curtis,Irving Reiner +1 more
TL;DR: In this paper, the authors present a group theory representation and modular representation for algebraic number theory, including Semi-Semi-Simple Rings and Group Algebras, including Frobenius Algebraic numbers.
Journal ArticleDOI
Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple
TL;DR: In this article, it was shown that the fourth power of the antipode is the identity in a finite-dimensional Hopf algebra over a field of characteristic 0, which is a conjecture mentioned by Kaplansky [I].
Journal ArticleDOI
Crossed products and inner actions of Hopf algebras
TL;DR: A theory of crossed products and inner (weak) actions of Hopf algebras on non-commutative groups was developed in this paper, which covers the usual examples of inner automorphisms and derivations, and in addition is general enough to include ''inner'' group gradings.
Journal ArticleDOI
Cleft comodule algebras for a bialgebra
Doi Yukio,Takeuchi Mitsuhiro +1 more
TL;DR: In this article, the Cleft comodule algebras for a bialgebra have been proposed for the first time, and they have been shown to be a good fit for a Bialgebra.