|
On idempotents in reduced enveloping algebras
Author(s):
George
B.
Seligman
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3291-3300.
MSC (2000):
Primary 17B35, 16S30
Posted:
April 17, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Explicit constructions are given for idempotents that generate all projective indecomposable modules for certain finite-dimensional quotients of the universal enveloping algebra of the Lie algebra  in odd prime characteristic. The program is put in a general context, although constructions are only carried through in the case of  .
References:
-
- [Ben]
- C. Bendel, Generalized reduced enveloping algebras for restricted Lie algebras, Journal of Algebra 218 (1999), 373-411. MR 2000h:17007
- [Ber]
- A. Berkson, The
 -algebra of a restricted Lie algebra is Frobenius, Proc. Amer. Math. Soc. 15 (1964), 14-15. MR 28:2132 - [C-R]
- C. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience (Wiley), New York (1962). MR 26:2519
- [J]
- N. Jacobson, Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience (Wiley), New York (1962); Dover edition, Dover Publications, New York 1979. MR 26:1345; MR 80k:17001
- [JCJ]
- J. C. Jantzen, Representations of Lie algebras in prime characteristic, In Representation Theories and Algebaic Geometry, A. Broer and A. Daigneault, eds., Kluwer, Dordrecht/Boston/London (1998), 185-235. MR 99h:17026
- [N]
- G. M. Nielsen, A Determination of the Minimal Right Ideals in the Enveloping Algebra of a Lie Algebra of Classical Type, Ph.D. dissertation, Madison, Wisconsin, 1963.
- [P]
- R. D. Pollack, Restricted Lie algebras of bounded type, Bull. Amer. Math. Soc. 74 (1968), 326-331. MR 36:2661
- [S]
- J. Schue, Symmetry for the enveloping algebra of a restricted Lie algebra, Proc. Amer. Math. Soc. 16 (1965), 1123-1124. MR 32:2515
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
17B35, 16S30
Retrieve articles in all Journals with MSC
(2000):
17B35, 16S30
Additional Information:
George
B.
Seligman
Affiliation:
Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
Email:
selig@math.yale.edu
DOI:
10.1090/S0002-9947-03-03314-2
PII:
S 0002-9947(03)03314-2
Received by editor(s):
August 14, 2002
Received by editor(s) in revised form:
January 15, 2003
Posted:
April 17, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org