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On central extensions of simple differential algebraic groups


Author: Andrey Minchenko
Journal: Proc. Amer. Math. Soc. 143 (2015), 2317-2330
MSC (2010): Primary 12H05; Secondary 19C09, 20G05, 13N10
DOI: https://doi.org/10.1090/S0002-9939-2015-12639-1
Published electronically: January 22, 2015
MathSciNet review: 3326014
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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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Additional Information

Andrey Minchenko
Affiliation: Faculty of Mathematics and Computer Science, Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001 Israel
Email: an.minchenko@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2015-12639-1
Received by editor(s): January 2, 2014
Published electronically: January 22, 2015
Additional Notes: The author was supported by the ISF grant 756/12 and by the Minerva Foundation with funding from the Federal German Ministry for Education and Research
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2015 American Mathematical Society