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Finite-Dimensional Hopf Algebras

Yuqiu Wei, Beishang Ren


This paper mainly discussed various characterizations for the finite-dimensional Hopf algebras over algebraically closed field and has characteristic 0. And further showed that the order of antipode of the Hopf algebras is finite, but also provides a hint on how to estimate the order of the antipodes.


Finite-dimensional Hopf algebras; Order of the antipode ; Trace; Semisimple; Cosemisimple; Eigenvalue; Distinguished grouplike

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[1] Sweedle M E. Hopf Algebra[M].New York Benamin;1969.

[2] Etingof, P. and Gelaki, S. On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic[J], Internat. Math. Res. Notices 1988.

[3] Radford D.E., The Structure of Hopf Algebras with a Projection[J], J.Algebra, 1985.

[4] Abe,E.Hopf Algebra[M].Cambridge Tracts in Mathematics 74,Cambridge University Press, Cambridge-New York;1980.

[5] Montgomery S.,Hopf Algebras and Their Actions on Rings[M],CBMS Reginal Conference Series in Math, 82,Amer.Math.Soc.,Porvidence,1993.

[6] Radford D.E., On the antipode of a cosemisimple Hopf algebra[J], J. Algebra,1985.

DOI: http://dx.doi.org/10.18686/ahe.v6i15.5134