On the Exponent of Finite-Dimensional Hopf Algebras

  title={On the Exponent of Finite-Dimensional Hopf Algebras},
  author={Pavel Etingof and Shlomo Gelaki},
We show that the exponent is invariant under twisting. We prove that for semisimple and cosemisimple Hopf algebras H, the exponent is finite and divides dim(H). For triangular Hopf algebras in characteristic zero, we show that the exponent divides dim(H). We conjecture that if H is semisimple and cosemisimple then the exponent always divides dim(H). These theorems and conjecture are motivated by the work of Kashina [Ka], who showed that (using our language) if the exponent of H divides dim(H… CONTINUE READING

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-9 of 9 references

Gelaki, On Finite-Dimensional Semisimple and Cosemisimple Hopf Algebras In Positive Characteristic

S. P. Etingof
International Mathematics Research Notices • 1998

Gelaki, Some Properties of Finite-Dimensional Semisimple Hopf Algebras

S. P. Etingof
Mathematical Research Letters • 1998

A Hopf algebra freeness theorem, Amer

NZ W.D. Nichols, M. B. Zoeller
J. of Math • 1989

A Hopf algebra freeness theorem

M. B. Zoeller
Amer . J . of Math . • 1988

Semenov-Tian-Shansky, Quantum R-matrices and factorization problems

M. N. Reshetikhin
J. Geometry and Physics • 1988

Towards Classification of Conformal Theories

C. Vafa
Phys. Lett. B • 1988

On antipodes in pointed Hopf algebras

TW E.J. Taft, R. L. Wilson
J. of Algebra • 1974

, Quantum Rmatrices and factorization problems

M. Semenov-Tian-Shansky
J . Geometry and Physics

Similar Papers

Loading similar papers…