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January, 2021 Higher deformations of Lie algebra representations I
Matthew WESTAWAY
J. Math. Soc. Japan 73(1): 221-261 (January, 2021). DOI: 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.

Funding Statement

The author was supported during this research by a PhD studentship from the Engineering and Physical Sciences Research Council.

Citation

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Matthew WESTAWAY. "Higher deformations of Lie algebra representations I." J. Math. Soc. Japan 73 (1) 221 - 261, January, 2021. https://doi.org/10.2969/jmsj/81188118

Information

Received: 29 August 2018; Revised: 19 September 2019; Published: January, 2021
First available in Project Euclid: 4 August 2020

Digital Object Identifier: 10.2969/jmsj/81188118

Subjects:
Primary: 17B10
Secondary: 17B35, 17B50

Rights: Copyright © 2021 Mathematical Society of Japan

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Vol.73 • No. 1 • January, 2021
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