Geodesic
Automorphic Lie Algebras and Cohomology of Root Systems
Journal of Lie theory, Tome 30 (2020) no. 1, pp. 59-84
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A cohomology theory of root systems emerges naturally in the context of Automorphic Lie Algebras, where it helps formulating some structure theory questions. In particular, one can find concrete models for an Automorphic Lie Algebra by integrating cocycles. In this paper we define this cohomology and show its connection with the theory of Automorphic Lie Algebras. Furthermore, we discuss its properties: we define the cup product, we show that it can be restricted to symmetric forms, that it is equivariant with respect to the automorphism group of the root system, and finally we show acyclicity at dimension two of the symmetric part, which is exactly what is needed to find concrete models for Automorphic Lie Algebras.
Classification : 17B05, 17B22, 17B65
Mots-clés : Cohomology of root systems, groupoid cohomology, automorphic Lie algebras, diagonal contractions, Cartan filtrations, generalised Inönü-Wigner contractions 
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     author = {V. Knibbeler and S. Lombardo and J. A. Sanders},
     title = {Automorphic {Lie} {Algebras} and {Cohomology} of {Root} {Systems}},
     journal = {Journal of Lie theory},
     pages = {59--84},
     year = {2020},
     volume = {30},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2020_30_1_JLT_2020_30_1_a5/}
}
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V. Knibbeler; S. Lombardo; J. A. Sanders. Automorphic Lie Algebras and Cohomology of Root Systems. Journal of Lie theory, Tome 30 (2020) no. 1, pp. 59-84. http://geodesic.mathdoc.fr/item/JLT_2020_30_1_JLT_2020_30_1_a5/