Pith. sign in

REVIEW 1 cited by

Classification and structure of generalized Legendrian racks

Not yet reviewed by Pith; the record is open.

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 2504.12671 v3 pith:6KYDDQOC submitted 2025-04-17 math.GT math.GRmath.QA

classification math.GTmath.GRmath.QA
keywords racksgl-rackslegendriancategoriescomputegeneralizedgl-quandlesmedial
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We study algebraic aspects of generalized Legendrian racks, which are nonassociative structures based on the Legendrian Reidemeister moves. We answer an open question characterizing the group of GL-structures on a given rack. As applications, we classify several infinite families of GL-racks. We also compute automorphism groups of dihedral GL-quandles. Then we compute the centers of the category of GL-racks and several of its full subcategories. We also construct an equivalence of categories between racks and GL-quandles. We also study tensor products of racks and GL-racks coming from universal algebra. Surprisingly, the categories of racks and GL-racks have tensor units. The induced symmetric monoidal structure on medial racks is closed, and similarly for medial GL-racks.

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. On medial Latin quandles and affine modules

    math.GR 2026-02 accept novelty 6.0 of 10

    As categories, Latin medial quandles are equivalent to affine modules over Z[t^{±1},(1−t)^{−1}], and medial commutative quandles to affine modules over Z[1/2].

Pith tools