Weyl groupoids with at most three objects

By Michael Cuntz, István Heckenberger. 2008

80 citations recorded by the source corpus.

Abstract We adapt the generalization of root systems by 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 the result that there exist infinitely many “standard”, but only 9 “exceptional” cases.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c515b2f110e56a12cf7cd7113a1fb6a0cd9b2d3a

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On finite dimensional Nichols algebras of diagonal type (2017, background): “Then every root hasmultiplicity one [35], so we can label the Lyndon words withΔq+; let lβ be the Lyndon word of degree β ∈ Δq+.”
Root systems and Weyl groupoids for Nichols algebras (2008, methodology): “. (4.3) implies that Li = {l(i)}which proves the lemma. 5. Weyl groupoids and root systems In this section we give the deﬁnition of generalized root systems in [HY08] in terms of category theory, see [CH08], and recall some results which will be needed in the following sections. Let I be a non-empty”
On finite-dimensional Hopf algebras (2014, background): “If these hold, then all roots are real [22]; we say that R is finite.”
Hopf Algebras and Root Systems (2020, result): “Most of the results in Part 2 have been already published in [ HY08 ], [ CH09b ], [ CH09a ], and [ CH12 ].”
On the Weak Order of Coxeter Groups (2011, background): “10 in this paper or the related and better studied groupoids such as as those in [21], [8], [20] (which is explictly concerned with weak order on Weyl groupoids) and [6].”