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An introduction to quasigroups and representations

An introduction to quasigroups and representations

Material type
Personal Author
Smith, Jonathan D. H. , 1949-.
Title Statement
An introduction to quasigroups and representations / Jonathan D.H. Smith.
Publication, Distribution, etc
Boca Raton, FL :   Chapman & Hall/CRC ,   2006.  
Physical Medium
xii, 340 p. ; 25 cm.
Series Statement
Studies in advanced mathematics
1584885378 (alk. paper)
Bibliography, Etc. Note
Includes bibliographical references and index.
Subject Added Entry-Topical Term
Quasigroups. Nonassociative algebras. Representations of groups.
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008 060912s2006 flu b 001 0 eng
010 ▼a 2006049290
020 ▼a 1584885378 (alk. paper)
024 3 1 ▼a 9781584885375
035 ▼a (KERIS)REF000012810049
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA181.5 ▼b .S65 2006
082 0 0 ▼a 512/.22 ▼2 22
090 ▼a 512.22 ▼b S653i
100 1 ▼a Smith, Jonathan D. H. , ▼d 1949-.
245 1 3 ▼a An introduction to quasigroups and representations / ▼c Jonathan D.H. Smith.
260 ▼a Boca Raton, FL : ▼b Chapman & Hall/CRC , ▼c 2006.
300 ▼a xii, 340 p. ; ▼c 25 cm.
490 0 ▼a Studies in advanced mathematics
504 ▼a Includes bibliographical references and index.
650 0 ▼a Quasigroups.
650 0 ▼a Nonassociative algebras.
650 0 ▼a Representations of groups.
945 ▼a KINS

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.22 S653i Accession No. 121139888 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

QUASIGROUPS AND LOOPS Latin squaresEquational quasigroups Conjugates Semisymmetry and homotopy Loops and piquesSteiner triple systems I Moufang loops and octonions Triality Normal formsExercises NotesMULTIPLICATION GROUPS Combinatorial multiplication groups Surjections The diagonal action Inner multiplication groups of piques Loop transversals and right quasigroupsLoop transversal codes Universal multiplication groups Universal stabilizers Exercises NotesCENTRAL QUASIGROUPS Quasigroup congruences Centrality NilpotenceCentral isotopy Central piques Central quasigroups Quasigroups of prime order Stability congruences No-go theorems Exercises NotesHOMOGENEOUS SPACES Quasigroup homogeneous spaces Approximate symmetry Macroscopic symmetry Regularity Lagrangean properties Exercises NotesPERMUTATION REPRESENTATIONS The category IFSQ Actions as coalgebras Irreducibility The covariety of Q-sets The Burnside algebra An example Idempotents Burnside's lemma Exercises Problems NotesCHARACTER TABLES Conjugacy classes Class functions The centralizer ring Convolution of class functions Bose-Mesner and Hecke algebras Quasigroup character tables Orthogonality relations Rank two quasigroups Entropy Exercises Problems NotesCOMBINATORIAL CHARACTER THEORY Congruence lattices Quotients FusionInduction Linear characters Exercises Problems NotesSCHEMES AND SUPERSCHEMES Sharp transitivityMore no-go theorems Superschemes Superalgebras Tensor squares Relation algebras The reconstruction theoremExercises Problems NotesPERMUTATION CHARACTERS Enveloping algebras Structure of enveloping algebras The canonical representation Commutative actions Faithful homogeneous spaces Characters of homogeneous spaces General permutation characters The Ising modelExercises Problems NotesMODULES Abelian groups and slice categories Quasigroup modules The fundamental theorem Differential calculusRepresentations in varieties Group representations ExercisesProblems NotesAPPLICATIONS OF MODULE THEORY Nonassociative powers Exponents Steiner triple systems II The Burnside problem A free commutative Moufang loop Extensions and cohomology Exercises ProblemsNotesANALYTICAL CHARACTER THEORY Functions on finite quasigroupsPeriodic functions on groups Analytical character theory Almost periodic functions Twisted translation operators Proof of the existence theorem Exercises Problems NotesAPPENDIX A: CATEGORICAL CONCEPTS Graphs and categoriesNatural transformations and functors Limits and colimits APPENDIX B: UNIVERSAL ALGEBRA Combinatorial universal algebra Categorical universal algebra APPENDIX C: COALGEBRAS Coalgebras and covarieties Set functors REFERENCES INDEX

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