Dupli�i, Stepan, <br/><br/>
Polyadic algebraic structures / 
Steven Duplij. 
 - 1 online resource (various pagings) :  illustrations. 
 - [IOP release $release] IOP ebooks. [2022 collection] .
 - IOP (Series).  Release 22. IOP ebooks.  2022 collection. .
<br/><br/> "Version: 20220601"--Title page verso. 
<br/><br/>Includes bibliographical references. 
<br/><br/>part I. One-set polyadic algebraic structures. 1. One-set algebraic structures and Hossz�u-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 Hossz�u-Gluskin theorem -- 1.5. Polyadic analog of Grothendieck group 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 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 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 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 6. Polyadic inner spaces and operators -- 6.1. Polyadic inner pairing spaces and norms -- 6.2. Elements of polyadic operator theory 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 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 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 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 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. 
<br/><br/> The book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century. 
<br/><br/> Computational physics, theoretical physics, mathematicians. 
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<br/><br/><br/>Mode of access: World Wide Web. <br/>System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader. 
<br/><br/><br/>Steven Duplij (Stepan Douplii) is a theoretical and mathematical physicist from the University of M�unster, 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. 
<br/><br/><label>ISBN: </label>9780750326483 9780750326476 
<br/><br/><label>Standard No.: </label>10.1088/978-0-7503-2648-3  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Algebra, Abstract.<br/>Polyadic algebras.<br/>Optimization.<br/>Mathematics and computation.
<br/><br/><label>LC Class. No.: </label>QA162  / .D877 2022eb 
<br/><br/><label>Dewey Class. No.: </label>512/.02