Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897277 | Journal of Pure and Applied Algebra | 2018 | 19 Pages |
Abstract
A quandle is an algebraic structure which attempts to generalize group conjugation. These structures have been studied extensively due to their connections with knot theory, algebraic combinatorics, and other fields. In this work, we approach the study of quandles from the perspective of the representation theory of categories. Namely, we look at collections of conjugacy classes of the symmetric groups and the finite general linear groups, and prove that they carry the structure of FI-quandles (resp. VIC(q)-quandles). As applications, we prove statements about the homology of these quandles, and construct FI-module and VIC(q)-module invariants of links.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Eric Ramos,