Vol. 301, No. 2, 2019

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Integration of modules I: stability

Dmitriy Rumynin and Matthew Westaway

Vol. 301 (2019), No. 2, 575–600
DOI: 10.2140/pjm.2019.301.575
Abstract

We explore the integration of representations from a Lie algebra to its algebraic group in positive characteristic. An integrable module is stable under the twists by group elements. Our aim is to investigate cohomological obstructions for passing from stability to an algebraic group action. As an application, we prove integrability of bricks for a semisimple algebraic group.

Keywords
Frobenius kernel, representation, cohomology, obstructions
Mathematical Subject Classification 2010
Primary: 20G05
Secondary: 17B45
Milestones
Received: 7 May 2018
Revised: 7 December 2018
Accepted: 27 December 2018
Published: 24 October 2019
Authors
Dmitriy Rumynin
Mathematics Institute
Zeeman Building
University of Warwick
Coventry
United Kingdom
Matthew Westaway
Mathematics Institute
Zeeman Building
University of Warwick
Coventry
United Kingdom