Invariant Hopf 2-Cocycles for Affine Algebraic Groups
Author(s)Etingof, Pavel I; Gelaki, Shlomo
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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  is bijective (unlike for some finite groups, as shown in ). 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 ).
International Mathematics Research Notices
Oxford University Press (OUP)
Pavel Etingof, and Shlomo Gelaki. "Invariant Hopf 2-Cocycles for Affine Algebraic Groups." International Mathematics Research Notices (March 2018) © The Authors 2018