An Introduction to Quasigroups and Their Representations

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CRC Press, 15 nov 2006 - 352 pagine
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.
 

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Indice

QUASIGROUPS AND LOOPS
1
MULTIPLICATION GROUPS
35
CENTRAL QUASIGROUPS
61
HOMOGENEOUS SPACES
93
PERMUTATION REPRESENTATIONS
113
CHARACTER TABLES
139
COMBINATORIAL CHARACTER THEORY
169
SCHEMES AND SUPERSCHEMES
199
MODULES
245
APPLICATIONS OF MODULE THEORY
265
ANALYTICAL CHARACTER THEORY
285
CATEGORICAL CONCEPTS
307
UNIVERSAL ALGEBRA
313
COALGEBRAS
317
References
319
Index
331

PERMUTATION CHARACTERS
225

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