A simplicial complex of Nichols algebras

A simplicial complex of Nichols algebras

We translate the concept of restriction of an arrangement in terms of Hopf algebras. In consequence, every Nichols algebra gives rise to a simplicial complex decorated by Nichols algebras with restricted root systems. As applications, some of these Nichols algebras provide Weyl groupoids which do no...

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Bibliographic Details
Published in:Mathematische Zeitschrift Vol. 285; no. 3-4; pp. 647 - 683
Main Authors: Cuntz, M., Lentner, S.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-04-2017
Springer Nature B.V
Subjects:
Algebra
Group theory
Mathematics
Mathematics and Statistics
Satake Diagram
Weyl Groupoid
Hopf Algebra
Finite Root System
Nichols Algebras
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Summary:We translate the concept of restriction of an arrangement in terms of Hopf algebras. In consequence, every Nichols algebra gives rise to a simplicial complex decorated by Nichols algebras with restricted root systems. As applications, some of these Nichols algebras provide Weyl groupoids which do not arise for diagonal Nichols algebras and in fact we realize all root systems of finite Weyl groupoids of rank greater than three. Further, our result explains the root systems of the folded Nichols algebras over nonabelian groups and of generalized Satake diagrams.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-016-1711-0