Derivations on quandle algebras

Abstract

The aim of this thesis is to outline the connection between quandles and knots and to build on the notion of derivation for quandle algebras. The first two chapters define and discuss racks and quandles, and rack rings and algebras. The third chapter is an overview of previously studied derivation algebras of quandle algebras, and the two final chapters investigate the derivation algebras of two types of conjugation quandles: the symmetric conjugation quandles and the dihedral conjugation quandles. We proved, that the derivation algebra of a conjugation quandle algebra with conjugacy classes obeys one symmetry and two sums. Furthermore, the derivation algebra of a 1dihedral conjugation quandle Dn algebra is trivial when n is odd.