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