New $R$-matrices for small quantum groups

Lentner, Simon; Nett, Daniel

doi:10.48550/arxiv.1409.5824

Search citation statements

Order By: Relevance

Paper Sections

Select...

Fourier Pairs Of {0 1}-matrices1

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

Publication Types

Select...

Other1

Relationship

Self Cite1

Independent0

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this application, the abelian group G will be the fundamental group of g, and hence cyclic except for g = D 2n . We will not discuss this matter further, but refer the reader to our respective paper [LN14]. Note Remark 5.4.…”

Section: Fourier Pairs Of {0 1}-matricesmentioning

confidence: 99%

See 1 more Smart Citation

A theorem on roots of unity and a combinatorial principle

Lentner,

Nett

2014

Preprint

Self Cite

View full text Add to dashboard Cite

Given a finite set of roots of unity, we show that all power sums are nonnegative integers iff the set forms a group under multiplication. The main argument is purely combinatorial and states that for an arbitrary finite set system the non-negativity of certain alternating sums is equivalent to the set system being a filter. As an application we determine all discrete Fourier pairs of {0, 1}-matrices. This technical result is an essential step in the classification of R-matrices of quantum groups.

show abstract

Section: Fourier Pairs Of {0 1}-matricesmentioning

confidence: 99%

“…Once these explicit solutions have been obtained, they can be plugged into the remaining equations which depend heavily on the specific parameters of the quantum group. This is done in a rather Lie-theoretic case-by-case argument in [LN14].…”

Section: Introductionmentioning

confidence: 99%