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Higher deformations of Lie algebra representations I
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Westaway, Matthew (2021) Higher deformations of Lie algebra representations I. Journal of the Mathematical Society of Japan, 73 (1). pp. 221-261. doi:10.2969/jmsj/81188118 ISSN 0025-5645.
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Official URL: https://doi.org/10.2969/jmsj/81188118
Abstract
In the late 1980s, Friedlander and Parshall studied the representations of a family of algebras which were obtained as deformations of the distribution algebra of the first Frobenius kernel of an algebraic group. The representation theory of these algebras tells us much about the representation theory of Lie algebras in positive characteristic. We develop an analogue of this family of algebras for the distribution algebras of the higher Frobenius kernels, answering a 30 year old question posed by Friedlander and Parshall. We also examine their representation theory in the case of the special linear group.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal of the Mathematical Society of Japan | ||||||||
Publisher: | Maths Society Japan | ||||||||
ISSN: | 0025-5645 | ||||||||
Official Date: | January 2021 | ||||||||
Dates: |
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Volume: | 73 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 221-261 | ||||||||
DOI: | 10.2969/jmsj/81188118 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 3 February 2020 | ||||||||
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