XMod
Authors:
Chris Wensley,
Murat Alp
Language:
GAP 4
Operating System:
Any
Current version:
2.010 (1.7 MB)
README file:
README (1 KB)
HTML:
chap0.html
(Version 2.005 provided the first complete functionality of the
GAP 3 version.)
Description
The XMod
package provides functions for computation with
finite crossed modules and cat1-groups
and their morphisms.
See the file notes.pdf
for an introductory account of these algebraic gadgets.
Crossed modules and cat1-groups are special types of
2-dimensional groups (see Ronnie Brown's web article
Higher Dimensional Group Theory),
and are implemented as 2dObjects.
The package divides into five parts,
the first four of which have been converted from
GAP 3.4.3 to the
GAP 4.4 release.
-
The first part is concerned with the standard constructions for
pre-crossed modules and crossed modules; together with
direct products; normal sub-crossed modules; and quotients.
Operations for constructing pre-cat1-groups and cat1-groups,
and for converting between cat1-groups and crossed modules,
are also included.
-
The second part is concerned with morphisms of (pre-)crossed modules
and (pre-)cat1-groups, together with standard operations for morphisms,
such as composition, image and kernel.
-
The third part deals with the equivalent notions of
derivation for a crossed module and section for a cat1-group,
and the monoids which they form under the Whitehead multiplication.
-
The fourth part deals with actor crossed modules and actor cat1-groups.
These are the automorphism objects in the appropriate categories.
For the actor crossed module
Act(X)
of a crossed module X
we require representations for the Whitehead group of regular derivations
of X and for the group of
automorphisms of X.
The construction also provides an inner morphism from
X
to Act(X) whose kernel
is the centre of X.
-
A new fifth part contains experimental functions for crossed squares
and their morhisms.
Manual
Choose from the following formats:
Authors
Chris Wensley
Mathematics Department
School of Informatics
University of Wales
Bangor, Gwynedd
LL57 1UT, UK
email:
c.d.wensley@bangor.ac.uk
Murat Alp
Dumlupinar Universitesi
Fen-Edebiyat Fakultesi
Matematik Bolumu
Merkez Kampus
Kutahya
Turkey
email:
malp@dumlupinar.edu.tr
How to cite XMod
M. Alp and C.D. Wensley,
XMod, a GAP4 package for crossed modules and cat1-groups,
version 2.010 (2007),
(http://www.informatics.bangor.ac.uk/public/mathematics/chda/xmod/).
GAP links:
(xmod2010.html, version 08/10/07)