An Introduction to Quasigroups and Their Representations

1. Auflage 2006
ISBN: 978-1-58488-537-5
Verlag: CRC Press

Buch, Englisch, 352 Seiten, Format (B × H): 166 mm x 235 mm, Gewicht: 621 g

Reihe: Studies in Advanced Mathematics

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.

Zielgruppe

Professional

Autoren/Hrsg.

Smith, Jonathan D. H.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Jonathan D. H. Smith