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Automorphic lie algebras and cohomology of root systems
journal contribution
posted on 2020-02-24, 10:09 authored by Vincent Knibbeler, Sara Lombardo, Jan A SandersThis 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 TheoryVolume
30Issue
1Pages
59 - 84Publisher
Heldermann VerlagVersion
- AM (Accepted Manuscript)
Rights holder
© Heldermann VerlagPublisher 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
2019-09-19Publication date
2020-03-01Copyright date
2020ISSN
0949-5932Publisher version
Language
- en