From the 1 of 10 linked papers with an AI index.
10 papers
Idempotents, automorphism groups, and commutator widths of quandle algebras
Birama Sangare, Luc Ta
The paper develops the theory of quandle algebras. We show that over integral domains of characteristic other than 2, quandle algebras of ordered commutative quandles have no nontr…
On medial Latin quandles and affine modules
Luc Ta
The paper shows that the categories of Latin and commutative medial quandles are equivalent to categories of affine modules over a Laurent polynomial ring and over the dyadic ratio…
Graph quandles: Generalized Cayley graphs of racks and right quasigroups
Luc Ta
This article lays the foundations for an analogue of geometric group theory that studies actions on graphs by right quasigroups, including racks and quandles. We study markings of…
Distinguishing Power of 4-Legendrian Permutation Racks
Luc Ta, Peyton Phinehas Wood
We study 4-Legendrian racks and their effectiveness at distinguishing Legendrian knots. We prove that permutation racks with 4-Legendrian rack structures cannot distinguish Legendr…
From affine algebraic racks to Leibniz algebras and Yang-Baxter operators
Luc Ta
We introduce analogues of algebraic groups called algebraic racks, which are pointed rack objects in the category of schemes over a ground field. Addressing a problem of Loday, we…
Groups versus quandle-like invariants of 3-manifolds
Luc Ta
Risandles are nonassociative algebraic structures recently introduced to construct invariants of 3-manifolds. In this note, we show that the categories of groups and nonempty, fait…