|
The second cohomology of simple  -modules
Author(s):
David
I.
Stewart
Journal:
Proc. Amer. Math. Soc.
138
(2010),
427-434.
MSC (2000):
Primary 20G05, 20G10, 20G40;
Secondary 20J06, 20C20
Posted:
September 14, 2009
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
Let  be the simple algebraic group  defined over an algebraically closed field  of characteristic  . In this paper, we compute the second cohomology of all irreducible representations of  .
References:
-
- 1.
- H. Andersen, J. C. Jantzen, Cohomology of induced representations for algebraic groups, Math. Ann. 269 (1984) 487-525. MR 766011 (86g:20057)
- 2.
- H. Andersen, J. Jørgensen and P. Landrock, The projective indecomposable modules of SL(2,
 ), Proc. London Math. Soc. (3) 46 (1983), no. 1, 38-52. MR 684821 (84f:20044) - 3.
- J. C. Jantzen, Representations of algebraic groups, Academic Press, Boston, MA, 1987. MR 899071 (89c:20001)
- 4.
- G. J. McNinch, The second cohomology of small irreducible modules for simple algebraic groups, Pacific Journal of Math. 204 (2002) 459-472. MR 1907901 (2003m:20062)
- 5.
- A. E. Parker, Higher extensions between modules for
 , Advances in Mathematics 209 (2007) 381-405. MR 2294227 (2008e:20071)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
20G05, 20G10, 20G40,
20J06, 20C20
Retrieve articles in all Journals with MSC
(2000):
20G05, 20G10, 20G40,
20J06, 20C20
Additional Information:
David
I.
Stewart
Affiliation:
Department of Mathematics, Imperial College, London, SW7 2AZ, United Kingdom
Email:
davis.stewart06@imperial.ac.uk
DOI:
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
Posted:
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
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org