Galois actions and blocks of tame infinitesimal group schemes

Farnsteiner, Rolf; Skowroński, Andrzej

doi:10.1090/S0002-9947-07-04124-4

Galois actions and blocks of tame infinitesimal group schemes
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Trans. Amer. Math. Soc. 359 (2007), 5867-5898 Request permission

Abstract:

Given an infinitesimal group $\mathcal {G}$, that is defined over an algebra- ically closed field of characteristic $p \ge 3$, we determine the block structure of the algebra of measures $H(\mathcal {G})$ in case its principal block $\mathcal {B}_0(\mathcal {G})$ is tame and the height of the factor group $\mathcal {G}/\mathcal {M}(\mathcal {G})$ of $\mathcal {G}$ by its multiplicative center $\mathcal {M}(\mathcal {G})$ is at least two. Our results yield a complete description of the stable Auslander-Reiten quiver of $H(\mathcal {G})$ along with a criterion for the domesticity of $H(\mathcal {G})$.

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