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Polycharacters of Cocommutative Hopf Algebras

Published online by Cambridge University Press:  20 November 2018

Yuri Bahturin ,
Mikhail Kochetov  and
Susan Montgomery
Yuri Bahturin
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NF, A1C 5S7, email: yuri@math.mun.ca
Mikhail Kochetov
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NF, A1C 5S7, email: mikhail@math.mun.ca
Susan Montgomery
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089-1113, USA, email: smontgom@math.usc.edu
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Abstract

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In this paper we extend a well-known theorem of M. Scheunert on skew-symmetric bicharacters of groups to the case of skew-symmetric bicharacters on arbitrary cocommutative Hopf algebras over a field of characteristic not 2. We also classify polycharacters on (restricted) enveloping algebras and bicharacters on divided power algebras.

Keywords

16W3016W55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 11 - 24
Copyright
Copyright © Canadian Mathematical Society 2002

References

[1] Bahturin, Y., Fischman, D. and Montgomery, S., Bicharacters, Twistings, and Scheunert's Theorem for Hopf Algebras. To appear.Google Scholar
[2] Montgomery, S., Hopf Algebras and their Actions on Rings. CBMS Regional Conference Series in Mathematics 82, AMS, Providence, RI, 1993.Google Scholar
[3] Serre, J.-P., Lie algebras and Lie groups. 1964 lectures given at Harvard University, 2nd edition. Lecture Notes in Mathematics 1500, Springer-Verlag, Berlin, 1992.Google Scholar
[4] Scheunert, M., Generalized Lie algebras. J. Math. Physics 20 (1979), 712–720.Google Scholar
[5] Sweedler, M., Hopf algebras with one grouplike element. Trans. Amer. Math. Soc. 127 (1967), 515–526.Google Scholar
[6] Sweedler, M., Weakening theorem on divided powers. Trans. Amer.Math. Soc. 154 (1971), 427–428.Google Scholar
[7] Zolotykh, A., Commutation factors and varieties of associative algebras. Fund. Prikl. Mat. 3 (1997), 453–468.Google Scholar