TY - JOUR
T1 - Asymptotic behaviors in the homology of symmetric group and finite general linear group quandles
AU - Ramos, Eric
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jpaa.2018.02.011
DO - 10.1016/j.jpaa.2018.02.011
M3 - Article
AN - SCOPUS:85041947911
SN - 0022-4049
VL - 222
SP - 3858
EP - 3876
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 12
ER -