File(s) under permanent embargo
Reason: Publisher requirement. Full text cannot be made available. Link to web page provided.
Automorphic lie algebras and cohomology of root systems
journal contributionposted on 2020-02-24, 10:09 authored by Vincent Knibbeler, Sara 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.
EPSRC (EP/E044646/1 and EP/E044646/2) and NWO (VENI 016.073.026)
- Mathematical Sciences
Published inJournal of Lie Theory
Pages59 - 84
- AM (Accepted Manuscript)
Rights holder© Heldermann Verlag
Publisher statementThis 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.