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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The second cohomology of simple $ SL_2$-modules


Author: David I. Stewart
Journal: Proc. Amer. Math. Soc. 138 (2010), 427-434
MSC (2000): Primary 20G05, 20G10, 20G40; Secondary 20J06, 20C20
Published electronically: September 14, 2009
MathSciNet review: 2557160
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Abstract: Let $ G$ be the simple algebraic group $ SL_2$ defined over an algebraically closed field $ K$ of characteristic $ p>0$. In this paper, we compute the second cohomology of all irreducible representations of $ G$.


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Additional Information

David I. Stewart
Affiliation: Department of Mathematics, Imperial College, London, SW7 2AZ, United Kingdom
Email: davis.stewart06@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10088-6
PII: S 0002-9939(09)10088-6
Keywords: Modular representation theory, algebraic groups, cohomology
Received by editor(s): April 3, 2009
Received by editor(s) in revised form: April 9, 2009
Published electronically: September 14, 2009
Additional Notes: This paper was prepared towards the author’s Ph.D. qualification under the supervision of Prof. M. W. Liebeck, with financial support from the EPSRC. We would like to thank Professor Liebeck for his help in producing this paper. Additional thanks are due to the anonymous referee, who made very helpful suggestions for improvements to the paper.
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.