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. The main idea was to take a single set, closed under one binary operation, and to 'generalize' it by increasing the arity of the operation, called a polyadic operation. Until now, a general approach to polyadic concrete many-set algebraic structures was absent. We propose to investigate algebraic structures in the 'concrete way' and provide consequent …
Read More ↓Title Statements
- Full title :Polyadic Algebraic Structures / Steven Duplij.
Summary
The book is devoted to the thorough study of polyadic (higher arity) algebraic structures, which has a long history, starting from 19th century. The main idea was to take a single set, closed under one binary operation, and to 'generalize' it by increasing the arity of the operation, called a polyadic operation. Until now, a general approach to polyadic concrete many-set algebraic structures was absent. We propose to investigate algebraic structures in the 'concrete way' and provide consequent 'polyadization' of each operation, starting from group-like structures and finishing with the Hopf algebra structures. Polyadic analogs of homomorphisms which change arity, heteromorphisms, are introduced and applied for constructing unusual representations, multiactions, matrix representations and polyadic analogs of direct product. We provide the polyadic generalization of the Yang-Baxter equation, find its constant solutions, and introduce polyadic tensor categories.
Read More ↓Edition Statements
- Publication Date:2022
Publication Statements
- Publisher(s):IOP Publishing
- Place of Publication:Bristol
- Language:eng
- Publication Date:2022
The Physical Object
- Description:online resource (xxiii, 64, 29, 48, 62, 40, 19, 22, 22, 56, 45, 30 sidor)
Edition Identifiers
- ISBN:9780750326483, 0750326484, 9780750326476, 0750326476
- DOI:10.1088/978-0-7503-2648-3
- oclc:on1333127453
- Dewey Decimal:512.02
Table of Contents
One-set algebraic structures and Hosszú-Gluskin theorem -- Representations and heteromorphisms -- Polyadic semigroups and higher regularity -- Polyadic rings, fields and integer numbers -- Polyadic algebras and deformations -- Polyadic inner spaces and operators -- Medial deformation of n-ary algebras -- Membership deformations and obscure n-ary algebras -- Polyadic Hopf algebras -- Solutions to higher braid equations -- Polyadic tensor categories
Read More ↓
Rate & Review