## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://intlpress.com/HHA/.
**

Extensions of racks and quandles
#
Extensions of racks and quandles

##
Nicholas Jackson

A \defn{rack} is a set equipped with a bijective,
self-right-distributivebinary operation, and a \defn{quandle} is a rack
which satisfies anidempotency condition.

In this paper, we introduce a new
definition of modules over a rack orquandle, and show that this definition
includes the one studied by Etingofand Gra\~na \cite{etingof/grana:orc} and
the more general one given byAndruskiewitsch and Gra\~na
\cite{andr/grana:pointed-hopf}. We furthershow that this definition
coincides with the appropriate specialisationof the definition developed
by Beck \cite{beck:thesis}, and hence thatthese objects form a suitable
category of coefficient objects in whichto develop homology and cohomology
theories for racks and quandles.

We then develop an Abelian extension theory
for racks and quandles whichcontains the variants developed by Carter,
Elhamdadi, Kamada andSaito \cite{carter/elhamdadi/saito:twisted,carter/kamada/saito:diag}
asspecial cases.

Homology, Homotopy and Applications, Vol. 7(2005), No. 1, pp. 151-167
http://www.rmi.acnet.ge/hha/volumes/2005/n1a8/v7n1a8.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2005/n1a8/v7n1a8.dvi (ps, dvi.gz, ps.gz, pdf)