Qualgebras and knotted 3-valent graphs
type: Dataset
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticspreprint
keyword: mathmath-atmathematics-mathalgebraic-topology-mathat
keyword: counting-invariants
keyword: qualgebras
keyword: quandles
keyword: knotted-3-valent-graphs
keyword: colorings
keyword: preprints-working-papers-
keyword: qualgebra-cohomology
keyword: squandles
keyword: boltzmann-weight
keyword: cocycle-invariants
landing page: https://hal.science/hal-00951712
description: This paper is devoted to qualgebras and squandles, which are quandles enriched with a compatible binary/unary operation. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. Topologically, qualgebras emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an ''algebraization'' of knots; squandles in turn simplify the qualgebra algebraization of graphs. Knotted 3-valent graph invariants are constructed by counting qualgebra/squandle colorings of graph diagrams, and are further enhanced using qualgebra/squandle 2-cocycles. Some algebraic properties and the beginning of a cohomology theory are given for both structures. A classification of size 4 qualgebras/squandles is presented, and their second cohomology groups are completely described.
issued: 2026-05-06T06:09:51.334332
language: en
modified: 2026-05-06T06:09:51.334337

test_moissonnage_selune
type: Agent

Qualgebras and knotted 3-valent graphs
type: Distribution
access URL: https://hal.science/hal-00951712
format: HTML
issued: 2026-05-06T06:09:51.352749
modified: 2026-05-06T06:09:51.312437