Invariant Hopf $2$-cocycles for affine algebraic groups
| Autor: | Shlomo Gelaki, Pavel Etingof |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics 01 natural sciences Noncommutative geometry Cohomology Mathematics - Quantum Algebra Bijection FOS: Mathematics Quantum Algebra (math.QA) Affine transformation 0101 mathematics Invariant (mathematics) Algebraic number Algebraically closed field Commutative property Mathematics |
| Zdroj: | arXiv |
| DOI: | 10.48550/arxiv.1707.08672 |
| Popis: | We generalize the theory of the second invariant cohomology group $H^2_{\rm inv}(G)$ for finite groups $G$, developed in [Da2,Da3,GK], to the case of affine algebraic groups $G$, using the methods of [EG1,EG2,G]. In particular, we show that for connected affine algebraic groups $G$ over an algebraically closed field of characteristic $0$, the map $\Theta$ from [GK] is bijective (unlike for some finite groups, as shown in [GK]). This allows us to compute $H^2_{\rm inv}(G)$ in this case, and in particular show that this group is commutative (while for finite groups it can be noncommutative, as shown in [GK]). Comment: 21 pages; added references |
| Databáze: | OpenAIRE |
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