On central extensions of simple differential algebraic groups

Minchenko, Andrey

doi:10.1090/S0002-9939-2015-12639-1

On central extensions of simple differential algebraic groups
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Proc. Amer. Math. Soc. 143 (2015), 2317-2330 Request permission

Abstract:

We consider central extensions $Z\hookrightarrow E\twoheadrightarrow G$ in the category of linear differential algebraic groups. We show that if $G$ is simple non-commutative and $Z$ is unipotent with the differential type smaller than that of $G$, then such an extension splits. We also give a construction of central extensions illustrating that the condition on differential types is important for splitting. Our results imply that non-commutative almost simple linear differential algebraic groups, introduced by Cassidy and Singer, are simple.

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