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

Published electronically:
January 22, 2015

MathSciNet review:
3326014

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Abstract: We consider central extensions in the category of linear differential algebraic groups. We show that if is simple non-commutative and is unipotent with the differential type smaller than that of , 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