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Automorphic lie algebras and cohomology of root systems

journal contribution
posted on 24.02.2020, 10:09 authored by Vincent KnibbelerVincent Knibbeler, Sara LombardoSara Lombardo, Jan A Sanders
This paper defines a cohomology theory of root systems which emerges naturally in the context of Automorphic Lie Algebras (ALiAs) but applies more generally to deformations of Lie algebras obtained by assigning a monomial in a finite number of variables to each weight vector. In the theory of Automorphic Lie Algebras certain problems can be formulated and partially solved in terms of cohomology, in particular one can find explicit models for an ALiA in terms of monomial deformations of the original Lie algebra. In this paper we formulate a cohomology theory of root systems and define the cup product in this context; we show that it can be restricted to symmetric forms, that it is equivariant with respect to the automorphism group of the original Lie algebra, and finally we show acyclicity at dimension two of the symmetric part, which is exactly what is needed to find models for ALiAs explicitly.

Funding

EPSRC (EP/E044646/1 and EP/E044646/2) and NWO (VENI 016.073.026)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Lie Theory

Volume

30

Issue

1

Pages

59 - 84

Publisher

Heldermann Verlag

Version

AM (Accepted Manuscript)

Rights holder

© Heldermann Verlag

Publisher statement

This paper was accepted for publication in the journal Journal of Lie Theory and the definitive published version is available at http://www.heldermann.de/JLT/JLT30/JLT301/jlt30006.htm.

Acceptance date

19/09/2019

Publication date

2020-03-01

Copyright date

2020

ISSN

0949-5932

Language

en

Depositor

Prof Sara Lombardo. Deposit date: 19 February 2020