Polyadic algebraic structures /

The book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Dupliæi, Stepan (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]
Colección:IOP (Series). Release 22.
IOP ebooks. 2022 collection.
Temas:
Algebra, Abstract.
Polyadic algebras.
Optimization.
Mathematics and computation.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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
  • 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.

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