Invariant Hopf 2-Cocycles for Affine Algebraic Groups
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 a...
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| Format: | Article |
| Language: | English |
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Oxford University Press (OUP)
2019
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| Online Access: | https://hdl.handle.net/1721.1/122973 |
| _version_ | 1826194529350320128 |
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| author | Etingof, Pavel I Gelaki, Shlomo |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I Gelaki, Shlomo |
| author_sort | Etingof, Pavel I |
| collection | MIT |
| description | 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]). |
| first_indexed | 2024-09-23T09:57:09Z |
| format | Article |
| id | mit-1721.1/122973 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:57:09Z |
| publishDate | 2019 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1229732024-06-14T12:24:53Z Invariant Hopf 2-Cocycles for Affine Algebraic Groups Etingof, Pavel I Gelaki, Shlomo Massachusetts Institute of Technology. Department of Mathematics 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]). 2019-11-20T14:05:24Z 2019-11-20T14:05:24Z 2018-03 2019-11-12T17:19:21Z Article http://purl.org/eprint/type/JournalArticle 1073-7928 1687-0247 https://hdl.handle.net/1721.1/122973 Pavel Etingof, and Shlomo Gelaki. "Invariant Hopf 2-Cocycles for Affine Algebraic Groups." International Mathematics Research Notices (March 2018) © The Authors 2018 en http://dx.doi.org/10.1093/imrn/rny025 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Etingof, Pavel I Gelaki, Shlomo Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title | Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title_full | Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title_fullStr | Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title_full_unstemmed | Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title_short | Invariant Hopf 2-Cocycles for Affine Algebraic Groups |
| title_sort | invariant hopf 2 cocycles for affine algebraic groups |
| url | https://hdl.handle.net/1721.1/122973 |
| work_keys_str_mv | AT etingofpaveli invarianthopf2cocyclesforaffinealgebraicgroups AT gelakishlomo invarianthopf2cocyclesforaffinealgebraicgroups |