Details
| Original language | English |
|---|---|
| Pages (from-to) | 647-683 |
| Number of pages | 37 |
| Journal | Mathematische Zeitschrift |
| Volume | 285 |
| Issue number | 3-4 |
| Publication status | Published - 1 Apr 2017 |
Abstract
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.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Mathematische Zeitschrift, Vol. 285, No. 3-4, 01.04.2017, p. 647-683.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A simplicial complex of Nichols algebras
AU - Cuntz, M.
AU - Lentner, S.
N1 - Funding information: S. Lentner is partly supported by the DFG Research Training Group 1670. Most results of this article were achieved at meetings supported by the DFG within the priority programme 1388.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84973597935&partnerID=8YFLogxK
U2 - 10.1007/s00209-016-1711-0
DO - 10.1007/s00209-016-1711-0
M3 - Article
AN - SCOPUS:84973597935
VL - 285
SP - 647
EP - 683
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -