Description
The book is devoted to the thorough study of polyadic(higher arity) algebraic structures, which has a long history, starting from 19thcentury. The main idea was to take a single set, closed under one binaryoperation, and to “generalize” it by increasing the arity of the operation,called a polyadic operation. Until now, a general approach to polyadic concretemany-set algebraic structures was absent. We propose to investigate algebraicstructures in the “concrete way” and provide consequent “polyadization” of eachoperation, starting from group-like structures and finishing with the Hopfalgebra structures. Polyadic analogs of homomorphisms which change arity,heteromorphisms, are introduced and applied for constructing unusualrepresentations, multiactions, matrix representations and polyadic analogs ofdirect product. We provide the polyadic generalization of the Yang-Baxterequation, find its constant solutions, and introduce polyadic tensorcategories.
Suitable for university students of advanced level algebracourses and mathematical physics. courses.
Key Features
- Provides a general, unifiedapproach
- Widens readers perspectiveof the possibilities to develop standard algebraic structures
- Provides the new kind ofhomomorphisms changing the arity, heteromorphisms, are introduced and appliedfor construction of new representations, multiactions and matrix representations
- Presents applications of“polyadization” approach to concrete algebraic structures
