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An introduction to quasigroups and their representations

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.T...

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Autor principal: Smith, Jonathan D H
Lenguaje:eng
Publicado: Taylor and Francis 2006
Materias:
Acceso en línea:http://cds.cern.ch/record/1991577
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author Smith, Jonathan D H
author_facet Smith, Jonathan D H
author_sort Smith, Jonathan D H
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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.
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spelling cern-19915772021-04-21T20:28:15Zhttp://cds.cern.ch/record/1991577engSmith, Jonathan D HAn introduction to quasigroups and their representationsMathematical Physics and MathematicsCollecting 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.Taylor and Francisoai:cds.cern.ch:19915772006
spellingShingle Mathematical Physics and Mathematics
Smith, Jonathan D H
An introduction to quasigroups and their representations
title An introduction to quasigroups and their representations
title_full An introduction to quasigroups and their representations
title_fullStr An introduction to quasigroups and their representations
title_full_unstemmed An introduction to quasigroups and their representations
title_short An introduction to quasigroups and their representations
title_sort introduction to quasigroups and their representations
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/1991577
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