Invariant Hopf 2-Cocycles for Affine Algebraic Groups
2018 ◽
Vol 2020
(2)
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pp. 344-366
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Abstract We generalize the theory of the second invariant cohomology group $H^{2}_{\textrm{inv}}(G)$ 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 $H^{2}_{\textrm{inv}}(G)$ in this case, and in particular show that this group is commutative (while for finite groups it can be noncommutative, as shown in [14]).
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1976 ◽
Vol 79
(3)
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pp. 401-425
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Keyword(s):
1996 ◽
pp. 1-120
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2012 ◽
Vol 11
(02)
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pp. 1250038
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1986 ◽
Vol 29
(4)
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pp. 469-477
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1979 ◽
Vol 27
(2)
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pp. 163-166
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2021 ◽
Vol 2021
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pp. 1-3