| Description |
1 online resource : illustrations |
| Contents |
Part I. One-set polyadic algebraic structures. 1. One-set algebraic structures and Hosszú-Gluskin theorem -- 1.1. General properties of one-set one-operation polyadic structures -- 1.2. Polyadic semigroups, quasigroups and groups -- 1.3. Polyadic direct products and changed arity powers -- 1.4. The deformed Hosszú-Gluskin theorem -- 1.5. Polyadic analog of Grothendieck group |
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2. Representations and heteromorphisms -- 2.1. Homomorphisms of one-set polyadic algebraic structures -- 2.2. Heteromorphisms of one-set polyadic algebraic structures -- 2.3. Hetero-covering of algebraic structures -- 2.4. Multiplace representations of polyadic algebraic structures -- 2.5. k-Place actions |
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3. Polyadic semigroups and higher regularity -- 3.1. Generalized q-regular elements in semigroups -- 3.2. Higher q-inverse semigroups -- 3.3. Higher q-inverse polyadic semigroups -- 3.4. Polyadic-binary correspondence, regular semigroups, braid groups |
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4. Polyadic rings, fields and integer numbers -- 4.1. One-set polyadic 'linear' structures -- 4.2. Polyadic direct products of rings and fields -- 4.3. Polyadic integer numbers -- 4.4. Finite polyadic rings of integers -- 4.5. Finite polyadic fields of integer numbers -- 4.6. Diophantine equations over polyadic integers and Fermat's theorem |
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Part II. Two-sets polyadic algebraic structures. 5. Polyadic algebras and deformations -- 5.1. Two-set polyadic structures -- 5.2. Mappings between polyadic vector spaces -- 5.3. Polyadic associative algebras |
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6. Polyadic inner spaces and operators -- 6.1. Polyadic inner pairing spaces and norms -- 6.2. Elements of polyadic operator theory |
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7. Medial deformation of n-ary algebras -- 7.1. Almost commutative graded algebra -- 7.2. Almost medial graded algebras -- 7.3. Medial n-ary algebras -- 7.4. Almost medial n-ary graded algebras -- 7.5. Toyoda's theorem for almost medial algebras |
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8. Membership deformations and obscure n-ary algebras -- 8.1. Graded algebras and Shur factors -- 8.2. Membership function and obscure algebras -- 8.3. Membership deformation of commutativity -- 8.4. Projective representations -- 8.5. n-ary double commutative algebras -- 8.6. Conclusions |
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Part III. Polyadic quantum groups. 9. Polyadic Hopf algebras -- 9.1. Polyadic coalgebras -- 9.2. Polyadic bialgebras -- 9.3. Polyadic Hopf algebras -- 9.4. Ternary examples -- 9.5. Polyadic almost co-commutativity and co-mediality |
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10. Solutions to higher braid equations -- 10.1. Yang-Baxter operators -- 10.2. Polyadic braid operators and higher braid equations -- 10.3. Solutions to the ternary braid equations |
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Part IV. Polyadic categories. 11. Polyadic tensor categories -- 11.1. Binary tensor categories -- 11.2. Polyadic tensor categories -- 11.3. Polyadic units, unitors and quertors -- 11.4. Braided tensor categories -- 11.5. Medialed polyadic tensor categories -- 11.6. Conclusions |
| Summary |
The book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century |
| Notes |
"Version: 20220601"--Title page verso |
| Bibliography |
Includes bibliographical references |
| Audience |
Computational physics, theoretical physics, mathematicians |
| Notes |
Steven Duplij (Stepan Douplii) is a theoretical and mathematical physicist from the University of Münster, Germany. Dr. Duplij is the editor-compiler of 'Concise Encyclopaedia of Supersymmetry' (2005, Springer), and is the author of more than a hundred scientific publications and several books. His scientific directions include supersymmetry and quantum groups, advanced algebraic structures, gravity and nonlinear electrodynamics, constrained systems and quantum computing |
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Title from PDF title page (viewed on July 5, 2022) |
| Subject |
Algebra, Abstract.
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Polyadic algebras.
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Optimization.
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Mathematics and computation.
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Algebra, Abstract
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Polyadic algebras
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| Form |
Electronic book
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| Author |
Institute of Physics (Great Britain), publisher.
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| ISBN |
0750326484 |
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9780750326476 |
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0750326476 |
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9780750326483 |
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