Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra

Alexander Thomas

Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra

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 2308.06158 v4 pith:ARF7YF3Z submitted 2023-08-11 math.QA math-phmath.MP

Alexander Thomas This is my paper · ORCID

classification math.QAmath-phmath.MP

keywords algebradeformedgroupmathfrakmodularoperatorswittacting

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

abstract

We describe new $q$-deformations of the 3-dimensional Heisenberg algebra, the simple Lie algebra $\mathfrak{sl}_2$ and the Witt algebra. They are constructed through a realization as differential operators. These operators are related to the modular group and $q$-deformed rational numbers defined by Morier-Genoud and Ovsienko and lead to $q$-deformed M\"obius transformations acting on the hyperbolic plane.

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

Nuancing the unicity of $q$-rationals
math.QA 2026-07 conditional novelty 6.0 of 10

Exactly two modular-group-equivariant deformations of rationals reproduce the standard q-integers, and the newly identified one has positive coefficients and directly yields Jones polynomials of rational knots.

Pith tools