Finite Dimensional Hopf Actions on Central Division Algebras
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1508.01251.pdf
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227.86 KB
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Author(s)
Cuadra-Diaz, Juan
Etingof, Pavel I
Date Issued
May 2016
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Cuadra, Juan and Pavel Etingof. “Finite Dimensional Hopf Actions on Central Division Algebras.” International Mathematics Research Notices 5, 1 (May 2016): 1562–1577 © 2016 The Author(s)
Version
Author's final manuscript
Abstract
Let k be an algebraically closed field of characteristic zero. Let D be a division algebra of degree d over its center Z(D). Assume that k. Z(D). We show that a finite group G faithfully grades D if and only if G contains a normal abelian subgroup of index dividing d. We also prove that if a finite dimensional Hopf algebra coacts on D defining a Hopf-Galois extension, then its PI degree is at most d². Finally, we construct Hopf-Galois actions on division algebras of twisted group algebras attached to bijective cocycles.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNW030
