The second cohomology of simple \(\text{SL}_2\)-modules. (English) Zbl 1204.20055
Let \(G\) be the algebraic group \(\text{SL}_2\) defined over an algebraically closed field \(K\) of characteristic \(p>0\). The author computes \(H^2(G,V)\) for every irreducible representation \(V\). The dimension of \(H^2(G,V)\) is either zero or one. The method is to study Hochschild-Serre spectral sequences with the first Frobenius kernel as normal subgroup scheme.
Reviewer: Wilberd van der Kallen (Utrecht)
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 20G10 | Cohomology theory for linear algebraic groups |
| 20C20 | Modular representations and characters |
Keywords:
modular representations; algebraic groups; special linear groups; cohomology groups; irreducible modules; dominant weights; spectral sequences; Frobenius kernelsReferences:
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