<Deleted> Catalogue of Algebraic Systems <Deleted>
The original Catalogue of Algebraic Systems was written by
John Pedersen. John moved and I inherited it. The catalogue was quite
incomplete. It had a few mistakes in it
and keeping it up was too much trouble. Meanwhile much more material on
algebraic systems has appeared on the web.
Below you will find some links where you might find what you are looking
for. Good luck! —W. Edwin Clark
recommend the following sites:
Most of the links
below were placed there sometime ago so don’t be surprised if they no
- Geoffrey Dixon's
Technical Pages on Division
Algebras (especially, Quaternions and Octonions), Lie Algebras, Lie
Groups, Spinors and Lattices
- To see how much we
have to add, browse: 1991
Mathematics Subject Classification
- Atlas of Finite
Group Representations. by Robert Wilson, et al.
- The Number of
Groups of Order n where n is at most 1000 and other Combinatorial Data. by
- GAP , Groups, Algorithms
and Programming, is a FREE system for computational discrete algebra with
particular emphasis on computational group theory. GAP includes various
databases including all groups of order up to 1,000, excluding 512 and
- Perhaps the most
general algebraic structure (outside of category theory) is the universal
algebra. For a brief introduction and some history see: Hermann
Grassmann and the Prehistory of Universal Algebra by Desmond
- Three element
groupoids. by Stanley
- Three element
groupoids with unary operation. by Stanley
Rusin's Algebraic Areas of Mathematics from his Mathematical Atlas This
itself contains quite a catalogue of algebraic systems.
Algebra Topics from the Math Forum's Internet Mathematics Library.
- Algebraic Systems This
is essentially a textbook on algebraic systems put together by Christer
Blomqvist. Compared to Weisstein's site above, this is more of a
tutorial. So take a look if you want more discussion. It is written in
English, but includes A very brief English to Swedish dictionary .
Homepage These groupoids are small categories where all morphism are
isomorphisms and are not to be confused with the other groupoids which
are sets with a single binary operation. See Ronald Brown's discussion of
groupoids in the
- Applied and
Computational Category Theory This includes a brief history and description
of category theory.
- Higher Dimensional
Group Theory By Ronald Brown.
- E. Lee Lady's Notes This
includes Notes on Homological Algegra, A Course in Abstract Algebra, and
Torsion Free Modules over Dedekind Domains.
Net Advance of Physics This is a list of links similar to the one you
are in now of topics of an algebraic nature--many, but not all, related
to physics. The list is compiled and managed by Norman Redington.
- Zero Divisor
Structure in Real Algebras by Steve Finch.
- Sketch of the
history of hypercomplex numbers Note that hypercomplex numbers are
better known as associative algebras .
- Logic and
Philosophy of Mathematics Section of Stanford's Encyclopedia of
Philosophy This includes entries for many interesting topics
including category theory and the home
page for the axiom of choice .
- Semigroup Mailing List
A mailing list to go to for technical questions about semigroups.
- Small Semigroups Reference to a paper on
the number of semigroups of orders up to 8 by S. Satoh, et al.
- Abstract Algebra On Line
This site contains many of the definitions and theorems from abstract
algebra. It is intended for undergraduate students taking an abstract
algebra class at the junior/senior level, as well as for students taking
their first graduate algebra course. It is based on the following books: Abstract
Algebra Second Edition, by John A. Beachy and William D. Blair, and Abstract
Algebra II, by John A. Beachy.
Rubik's cube group ( which has order 43252003274489856000) from the
homepage of W. D.
Joyner which links to Joyner's Permutation Puzzle Page and
other algebraic matters of interest.
- Rubik's Cube Page
A LOT of Rubik's cube information by Michael
- Rubik's Cube Solutions by Josef
"Gloom" Jelinek and Dr. Hana M. Bizek.
Worksheets for Abstract Algebra This is a collection of Maple
worksheets by Fr Mike May, S.J. The worksheets are mainly concerned with
field theory--Galois theory, finite fields, etc.
- Diamond Theory by Steven H. Cullinane.
See also The Diamond 16
Puzzle also by Steven Cullinane. The puzzle displays the affine group
on the 4-space over GF(2) as generated by row/column/quadrant
permutations of a 4x4 array.
- Exploring Abstract Algebra with
Mathematica by Al Hibbard and Ken Levasseur. This is a
collection of Mathematica packages that enable one to work with concepts
from abstract algebra (including groups, rings, fields, and morphisms).