An introduction to quasigroups and their representations. (©2007)

• Record Type: Book
• Further Information: Note: Jonathan D.H. Smith.
• Other Names: Smith, Jonathan D. H, 1949-
• Contents: QUASIGROUPS AND LOOPS; Latin squares; Equational quasigroups; Conjugates; Semisymmetry and homotopy; Loops and piques; Steiner triple systems I; Moufang loops and octonions; Triality; Normal forms; Exercises; Notes; ; MULTIPLICATION GROUPS; Combinatorial multiplication groups; Surjections; The diagonal action; Inner multiplication groups of piques; Loop transversals and right quasigroups; Loop transversal codes; Universal multiplication groups; Universal stabilizers; Exercises; Notes; ; CENTRAL QUASIGROUPS; Quasigroup congruences; Centrality; Nilpotence; Central isotopy; Central piques; Central quasigroups; Quasigroups of prime order; Stability congruences; No-go theorems; Exercises; Notes; ; HOMOGENEOUS SPACES; Quasigroup homogeneous spaces; Approximate symmetry; Macroscopic symmetry; Regularity; Lagrangean properties; Exercises; Notes; ; PERMUTATION REPRESENTATIONS; The category IFSQ; Actions as coalgebras; Irreducibility; The covariety of Q-sets; The Burnside algebra; An example; Idempotents; Burnside's lemma; Exercises; Problems; Notes; ; CHARACTER 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; Notes; ; COMBINATORIAL CHARACTER THEORY; Congruence lattices; Quotients; Fusion; Induction; Linear characters; Exercises; Problems; Notes; ; SCHEMES AND SUPERSCHEMES; Sharp transitivity; More no-go theorems; Superschemes; Superalgebras; Tensor squares; Relation algebras; The reconstruction theorem; Exercises; Problems; Notes; ; PERMUTATION CHARACTERS; Enveloping algebras; Structure of enveloping algebras; The canonical representation; Commutative actions; Faithful homogeneous spaces; Characters of homogeneous spaces; General permutation characters; The Ising model; Exercises; Problems; Notes; ; MODULES; Abelian groups and slice categories; Quasigroup modules; The fundamental theorem; Differential calculus; Representations in varieties; Group representations; Exercises; Problems; Notes; ; APPLICATIONS OF MODULE THEORY; Nonassociative powers; Exponents; Steiner triple systems II; The Burnside problem; A free commutative Moufang loop; Extensions and cohomology; Exercises; Problems; Notes; ; ANALYTICAL CHARACTER THEORY; Functions on finite quasigroups; Periodic functions on groups; Analytical character theory; Almost periodic functions; Twisted translation operators; Proof of the existence theorem; Exercises; Problems; Notes; ; APPENDIX A: CATEGORICAL CONCEPTS; Graphs and categories; Natural 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
• Publisher Details: Boca Raton, FL : Chapman & Hall/CRC
• Publication Date: 2007
• Copyright Date: 2007
• Extent: 1 online resource (xii, 340 pages), illustrations
• Subjects: 512/.22; Quasigroups; Nonassociative algebras; Representations of groups; Quasi-groupes; Algèbres non associatives; Représentations de groupes; MATHEMATICS -- Group Theory; Nonassociative algebras; Quasigroups; Representations of groups; Electronic books
• Languages: English
• ISBNs: 9781420010633; 1420010638; 1584885378; 9781584885375
• Notes: Note: Includes bibliographical references (pages 319-329) and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.