Zero Product Determined Algebras

This book provides a comprehensive survey of the theory of zero product-determined algebras,divided into three parts: algebraic,functional analytic,and applications. It is intended for researchers and graduate students in ring theory,Banach algebra theory,and nonassociative algebra.

Format: Paperback / softback
Length: 185 pages
Publication date: 26 August 2021
Publisher: Springer Nature Switzerland AG

This comprehensive volume offers a thorough exploration of the theory of zero product-determined algebras, a field that has seen significant advancements in the past 15 years. Comprising three distinct sections, it provides a comprehensive overview of this field. The first part delves into the purely algebraic aspects, while the second part explores the functional analytic branch. Additionally, the third part explores various applications of these algebras. Designed for researchers and advanced graduate students in ring theory, Banach algebra theory, and nonassociative algebra, this book offers valuable insights into the latest developments and applications in this area.

Introduction:
The theory of zero product-determined algebras has emerged as a vital area of study in modern mathematics, with applications in various fields such as ring theory, Banach algebra theory, and nonassociative algebra. This book aims to provide a concise survey of this theory, covering its fundamental concepts, results, and applications.
Part I: Purely Algebraic Branch:
The first part of the book focuses on the purely algebraic aspects of zero product-determined algebras. It begins by introducing the necessary definitions and notations, and then proceeds to explore the basic properties and structures of these algebras. The authors discuss various topics such as homomorphisms, ideals, modules, and coalgebras, and illustrate their concepts with examples and exercises.
Part II: Functional Analytic Branch:
The second part of the book delves into the functional analytic branch of zero product-determined algebras. It begins by discussing the concept of Banach algebras and their properties, including the norm, the dual space, and the Stone representation. The authors then introduce the notion of zero product-determined algebras and discuss their basic properties, such as the zero divisors, the annihilator, and the center. They also explore the relationship between zero product-determined algebras and other types of algebras, such as Banach algebras and Lie algebras.
Part III: Applications:
The third part of the book discusses various applications of zero product-determined algebras. It begins by discussing the representation theory of zero product-determined algebras, including the representation of finite groups and the representation theory of compact Lie groups. The authors then explore the applications of zero product-determined algebras in the theory of operator algebras, including the theory of C*-algebras and the theory of von Neumann algebras. Additionally, they discuss the applications of zero product-determined algebras in the theory of quantum groups and the theory of noncommutative geometry.
Conclusion:
In conclusion, this book provides a comprehensive survey of the theory of zero product-determined algebras, covering its purely algebraic, functional analytic, and applications aspects. It is intended for researchers and advanced graduate students in ring theory, Banach algebra theory, and nonassociative algebra. By presenting the latest developments and insights in this field, this book will be a valuable resource for anyone interested in studying zero product-determined algebras.

Weight: 358g
Dimension: 169 x 240 x 16 (mm)
ISBN-13: 9783030802417
Edition number: 1st ed. 2021