Pith. sign in

REVIEW 1 cited by

The hyperoctahedral quantum group

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv math/0701859 v2 pith:GJHFWLKG submitted 2007-01-29 math.RT

Teodor Banica , Julien Bichon , Benoit Collins This is my paper · ORCID
classification math.RT
keywords groupquantumconsidersymmetrydeformationdenotedenlargesformed
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We consider the hypercube in $\mathbb R^n$, and show that its quantum symmetry group is a $q$-deformation of $O_n$ at $q=-1$. Then we consider the graph formed by $n$ segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted $H_n^+$, enlarges Wang's series $S_n^+,O_n^+,U_n^+$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A Hopf algebra on permutations with a coupling product

    math.CO 2026-07 conditional novelty 6.0 of 10

    A new coupling product and draw coproduct make the vector space of permutations into a graded, connected, cocommutative, free Hopf algebra with a monomial-basis-like presentation.

Pith tools