Involutory Hopf algebras
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- by D. S. Passman and Declan Quinn PDF
- Trans. Amer. Math. Soc. 347 (1995), 2657-2668 Request permission
Abstract:
In 1975, Kaplansky conjectured that a finite-dimensional semisimple Hopf algebra is necessarily involutory. Twelve years later, Larson and Radford proved the conjecture in characterisitic $0$ and obtained significant partial results in positive characteristics. The goal of this paper is to offer an efficient proof of these results using rather minimal prerequisites, no "harpoons", and gratifyingly few "hits".References
- Irving Kaplansky, Bialgebras, Lecture Notes in Mathematics, University of Chicago, Department of Mathematics, Chicago, Ill., 1975. MR 0435126
- Richard Gustavus Larson, Characters of Hopf algebras, J. Algebra 17 (1971), 352–368. MR 283054, DOI 10.1016/0021-8693(71)90018-4
- Richard G. Larson and David E. Radford, Finite-dimensional cosemisimple Hopf algebras in characteristic $0$ are semisimple, J. Algebra 117 (1988), no. 2, 267–289. MR 957441, DOI 10.1016/0021-8693(88)90107-X
- Richard G. Larson and David E. Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 110 (1988), no. 1, 187–195. MR 926744, DOI 10.2307/2374545
- Warren D. Nichols, Cosemisimple Hopf algebras, Advances in Hopf algebras (Chicago, IL, 1992) Lecture Notes in Pure and Appl. Math., vol. 158, Dekker, New York, 1994, pp. 135–151. MR 1289424
- David E. Radford, The group of automorphisms of a semisimple Hopf algebra over a field of characteristic $0$ is finite, Amer. J. Math. 112 (1990), no. 2, 331–357. MR 1047302, DOI 10.2307/2374718
- David E. Radford, The trace function and Hopf algebras, J. Algebra 163 (1994), no. 3, 583–622. MR 1265853, DOI 10.1006/jabr.1994.1033
- Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 2657-2668
- MSC: Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9947-1995-1283560-3
- MathSciNet review: 1283560