Extensions of racks and quandles

Abstract

New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is shown to coincide with Beck's general definition of a module in an arbitrary category. A theory of Abelian extensions of racks and quandles is then developed, which is shown to generalise the theories developed by Carter, Elhamdadi, Kamada and Saito.

v1: 18 pages, LaTeX2e, uses diagram.sty and gtart.cls (included). v2: Three typographical errors corrected. v3: 17 pages, LaTeX2e, uses diagxy.sty and hha.cls (included), Example 2.3 expanded, full proof of Theorem 2.3, several typographical errors and typesetting issues addressed