2006/11/28 by Daisy Lam, Lam, Daisy, Sam Nelson +1
Chemistry · Mathematics · #17D99 #57M25 #57M27 #Algebraic structures and combinatorial models #Bijection #Chemistry #Combinatorics #Coset #Crystal structure #Crystallography #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematics #Pure mathematics #Quantum Algebra (math.QA) #math.GT #math.QA #msc:17D99 #msc:57M25 #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0611887
10 pages. Version 2 includes changes suggested by referee, including a title change. To appear in Intl. J. Math
openalex publication_date 2006/11/28 · arxiv created 2007/12/21 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that two Alexander biquandles M and M' are isomorphic iff there is an isomorphism of Z[s,1/s,t,1/t]-modules h:(1-st)M --> (1-st)M' and a bijection g:Os(A) --> Os(A') between the s-orbits of sets of coset representatives of M/(1-st)M and M'/(1-st)M' respectively satisfying certain compatibility conditions.