Finite-Dimensional Hopf Algebras
Abstract
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.References
[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.
Authors contributing to this journal agree to publish their articles under the Creative Commons Attribution-Noncommercial 4.0 International License, allowing third parties to share their work (copy, distribute, transmit) and to adapt it, under the condition that the authors are given credit, that the work is not used for commercial purposes, and that in the event of reuse or distribution, the terms of this license are made clear. With this license, the authors hold the copyright without restrictions and are allowed to retain publishing rights without restrictions as long as this journal is the original publisher of the articles.
