The Cocycle structure of the Alexander $f$-quandles on finite fields

Abstract

We determine the second, third, and fourth cohomology groups of Alexander $f$-quandles of the form ${\mathbb{F}}_q[T,S]/(T-\omega ,S-\beta )$, where ${\mathbb{F}}_q$ denotes the finite field of order $q$, $\omega \in {\mathbb{F}}_q\setminus \{0,1\}$, and $\beta \in {\mathbb{F}}_q$

18 pages, comments are welcome