Synopsis
Various algebraic structures are investigated from the viewpoint that the initial arities of all operations are arbitrary ("polyadization" and partial arity freedom principle), and the relations between operations, arising from the structure definitions, lead to restrictions of their arity shapes ("quantization"). This unified procedure is applied to one-set and two-set algebraic structures, as well as to Hopf algebras and tensor categories, which gives new unusual properties and enriched objects absent in the ordinary binary structures.
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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.
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Hardcover. Condition: new. Hardcover. 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 FeaturesProvides 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 representationsPresents applications ofpolyadization approach to concrete algebraic structures Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780750326469
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