
An Introduction to Quasigroups and Their Representations
Jonathan D. H. Smith(Author)
Chapman & Hall/CRC (Publisher)
1st Edition
Published on 15. November 2006
Book
Hardback
352 pages
978-1-58488-537-5 (ISBN)
Description
Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension.
To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters deal with the three main branches of representation theory-permutation representations of quasigroups, combinatorial character theory, and quasigroup module theory. Each chapter includes exercises and examples to demonstrate how the theories discussed relate to practical applications. The book concludes with appendices that summarize some essential topics from category theory, universal algebra, and coalgebras.
Long overshadowed by general group theory, quasigroups have become increasingly important in combinatorics, cryptography, algebra, and physics. Covering key research problems, An Introduction to Quasigroups and Their Representations proves that you can apply group representation theories to quasigroups as well.
To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters deal with the three main branches of representation theory-permutation representations of quasigroups, combinatorial character theory, and quasigroup module theory. Each chapter includes exercises and examples to demonstrate how the theories discussed relate to practical applications. The book concludes with appendices that summarize some essential topics from category theory, universal algebra, and coalgebras.
Long overshadowed by general group theory, quasigroups have become increasingly important in combinatorics, cryptography, algebra, and physics. Covering key research problems, An Introduction to Quasigroups and Their Representations proves that you can apply group representation theories to quasigroups as well.
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional
Illustrations
14 s/w Abbildungen
14 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 156 mm
Weight
810 gr
ISBN-13
978-1-58488-537-5 (9781584885375)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Jonathan D. H. Smith
An Introduction to Quasigroups and Their Representations
E-Book
11/2006
Chapman & Hall/CRC
€225.99
Available for download

Jonathan D. H. Smith
An Introduction to Quasigroups and Their Representations
E-Book
11/2006
Chapman and Hall
€225.99
Available for download
Person
Jonathan D. H. Smith
Content
Quasigroups and Loops. Multiplications Groups. Central Quasigroups. Homogeneous Spaces. Permutation Representations. Character Tables. Combinatorial Character Theory. Schemes and Superschemes. Permutation Characters. Modules. Applications of Module Theory. Analytical Character Theory. Appendices. References. Index.