Polyadic Algebraic Structures - Hardcover

Duplij, Steven

Hardcover

ISBN 10: 0750326468 ISBN 13: 9780750326469

Publisher: Iop Publishing Ltd, 2022

Synopsis

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

About this title

About the Author

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.

Edition details

• Publisher: Iop Publishing Ltd
• Publication date: 2022
• Language: English
• ISBN 10: 0750326468
• ISBN 13: 9780750326469
• Binding: Hardcover
• Number of pages: 250