Journal ArticleDOI
On generalizations of root systems
TLDR
In this paper, the authors define a generalization of a root system as a set of vectors in a vector space with some symmetry property, and classify irreducible generalized root systems.Abstract:
We define a generalization of a root system as a set of vectors in a vector space with some symmetry property. The main difference with the usual root systems is the existence of isotropic roots. We classify irreducible generalized root systems. As follows from our classification all such root systems are root systems of contragredient Lie superalgebras which were classified by V.Kac in 1977.read more
Citations
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Journal ArticleDOI
Deformed Quantum Calogero-Moser Problems and Lie Superalgebras
TL;DR: In this article, the deformed quantum Calogero-Moser-Sutherland problems related to root systems of the contragredient Lie superalgebras are introduced.
Journal ArticleDOI
A generalization of Coxeter groups, root systems, and Matsumoto’s theorem
TL;DR: In this article, the authors show that the symmetry object of the Weyl group is generated by simple reflections and Coxeter relations, and that the weak version of the exchange condition for the groupoid is solved.
Journal ArticleDOI
Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type
TL;DR: In this article, the authors defined the Drinfel double for a class of graded Hopf algebras, including small quantum groups and multiparameter quantizations of semisimple Lie superalgesas.
Book ChapterDOI
On Nichols Algebras with Generic Braiding
TL;DR: In this paper, the authors extend the main result of [AS3] to braided vector spaces of generic diagonal type using results of Heckenberger, and they extend the result of AS3 to Braided Vector Spaces with generic diagonal types.
Posted Content
A generalization of Coxeter groups, root systems, and Matsumoto's theorem
TL;DR: In this paper, the authors show that the symmetry object of the Weyl group is generated by reflections and Coxeter relations, which is a weak version of the exchange condition that allows them to prove Matsumoto's theorem.
References
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Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.