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Abstract
Humphreys' conjecture on blocks parametrises the blocks of a reduced enveloping algebra of the Lie algebras of a reductive algebraic group over an algebraically closed field of positive characteristic. It is well-known to hold under Jantzen's standard assumptions. We note here that it holds under slightly weaker assumptions, by utilising the full generality of certain results in the literature. We also provide a new approach to prove the result in type G_2 in characteristic 3, a case in which the previously mentioned weaker assumptions do not hold. This approach requires some dimensional calculations for certain centralisers, which we conduct in the Appendix for all the exceptional Lie algebras in bad characteristic.
Original language | English |
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Number of pages | 20 |
Journal | Algebras and Representation Theory |
Volume | 2022 |
Early online date | 19 Dec 2022 |
DOIs | |
Publication status | E-pub ahead of print - 19 Dec 2022 |
Keywords
- Reduced enveloping algebras
- block decomposition
- Lie algebras
- Humphreys' conjecture
ASJC Scopus subject areas
- Algebra and Number Theory
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Dive into the research topics of 'A note on Humphreys' conjecture on blocks'. Together they form a unique fingerprint.Projects
- 1 Finished
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Representation theory of modular Lie algebras and superalgebras
Goodwin, S. (Principal Investigator)
Engineering & Physical Science Research Council
1/07/18 → 31/12/22
Project: Research Councils