Mini-Workshop: Nichols Algebras and Weyl Groupoids
نویسندگان
چکیده
منابع مشابه
Geometric combinatorics of Weyl groupoids
We extend properties of the weak order on finite Coxeter groups to Weyl groupoids admitting a finite root system. In particular, we determine the topological structure of intervals with respect to weak order, and show that the set of morphisms with fixed target object forms an ortho-complemented meet semilattice. We define the Coxeter complex of a Weyl groupoid with finite root system and show ...
متن کاملRight Coideal Subalgebras of Nichols Algebras and the Duflo Order on the Weyl Groupoid
We study graded right coideal subalgebras of Nichols algebras of semisimple Yetter-Drinfeld modules. Assuming that the Yetter-Drinfeld module admits all reflections and the Nichols algebra is decomposable, we construct an injective order preserving and order reflecting map between morphisms of the Weyl groupoid and graded right coideal subalgebras of the Nichols algebra. Here morphisms are orde...
متن کاملWEYL ALGEBRAS and KNOTS
ABSTRACT In this paper we push forward results on the invariant F -module of a virtual knot investigated by the first named author where F is the algebra with two invertible generators A,B and one relation ABAB −BAB = BABA− A . For flat knots and links the two sides of the relation equation are put equal to unity and the algebra becomes the Weyl algebra. If this is perturbed and the two sides o...
متن کاملWeyl Groupoids with at Most Three Objects
We adapt the generalization of root systems of the second author and H. Yamane to the terminology of category theory. We introduce Cartan schemes, associated root systems and Weyl groupoids. After some preliminary general results, we completely classify all finite Weyl groupoids with at most three objects. The classification yields that there exist infinitely many “standard”, but only 9 “except...
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ژورنال
عنوان ژورنال: Oberwolfach Reports
سال: 2012
ISSN: 1660-8933
DOI: 10.4171/owr/2012/47