Invariant Hopf 2-Cocycles for Affine Algebraic Groups
Name
1707.08672.pdf
Description
Submitted version
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257.87 KB
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Adobe PDF
Checksum (MD5)
2ed2a99f33dcbb924e8a6b2e3a4d9503
Author(s)
Etingof, Pavel I
Gelaki, Shlomo
Date Issued
March 2018
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Citation
Pavel Etingof, and Shlomo Gelaki. "Invariant Hopf 2-Cocycles for Affine Algebraic Groups." International Mathematics Research Notices (March 2018) © The Authors 2018
Version
Original manuscript
Abstract
We generalize the theory of the second invariant cohomology group H[superscript 2][subscript inv](G) for finite groups G, developed in [3, 4, 14], to the case of affine algebraic groups G, using the methods of [9, 10, 12]. In particular, we show that for connected affine algebraic groups G over an algebraically closed field of characteristic 0, the map Θ from [14] is bijective (unlike for some finite groups, as shown in [14]). This allows us to compute H[superscript 2][subscript inv](G) in this case, and in particular show that this group is commutative (while for finite groups it can be noncommutative, as shown in [14]).
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/rny025
