Polyadic Algebraic Structures

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Steven Duplij (Doctor of Physical and Mathematical Sciences, University of Münster (Germany))

Polyadic Algebraic Structures

Steven Duplij (Doctor of Physical and Mathematical Sciences, University of Münster (Germany))

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English

Institute of Physics Publishing
07 June 2022

Groups & group theory; Optimisation; States of matter

Series: IOP ebooks

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.

Suitable for university students of advanced level algebra courses and mathematical physics courses.

Key Features

Provides a general, unified approach

Widens readers perspective of the possibilities to develop standard algebraic structures

Provides the new kind of homomorphisms changing the arity, heteromorphisms, are introduced and applied for construction of new representations, multiactions and matrix representations

Presents applications of “polyadization” approach to concrete algebraic structures

By: Steven Duplij (Doctor of Physical and Mathematical Sciences University of Münster (Germany))
Imprint: Institute of Physics Publishing
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm, Spine: 25mm
Weight: 1.018kg
ISBN: 9780750326469
ISBN 10: 0750326468
Series: IOP ebooks
Pages: 464
Publication Date: 07 June 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Contents Preface Acknowledgements About the Author Symbols Introduction Bibliography Main ideas and new constructions One-set polyadic algebraic structures One-set algebraic structures and Hosszu-Gluskin theorem Representations and heteromorphisms Polyadic semigroups and higher regularity Polyadic rings, fields and integer numbers Two-sets polyadic algebraic structures Polyadic algebras and deformations Polyadic inner spaces and operators Medial deformation of n-ary algebras Membership deformations and obscure n-ary algebras Polyadic quantum groups Polyadic Hopf algebras Solutions to higher braid equations Polyadic categories Polyadic tensor categories Bibliography

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.