The Cohomology of Commutative Semigroups: An Overview

The book provides an organized exposition of commutative semigroup cohomology, compares approaches, addresses higher-dimensional problems, and reviews computational methods. It will be a valuable resource for students and researchers in the field.

Format: Paperback / softback
Length: 179 pages
Publication date: 10 September 2022
Publisher: Springer International Publishing AG

This comprehensive book offers a thorough and organized exploration of the current state of commutative semigroup cohomology, a theory that the author has pioneered and has seen significant development in recent years. Within its pages, readers will find a fundamental scientific investigation into a wide range of questions within this field. The book compares and contrasts different approaches to commutative semigroup cohomology, addressing the challenges posed by definitions in higher dimensions. It also provides a comprehensive review of computational methods employed in this area.

The primary focus of the book is on the computation of extensions of commutative semigroups and their classification. Prior to its publication, the components of this theory were scattered across various research articles. This work brings all these elements together in a single, convenient volume, making it an invaluable resource for future students and researchers interested in commutative semigroup cohomology and related areas.

The book is structured in a clear and accessible manner, with each chapter providing a comprehensive overview of the relevant topics. It begins by introducing the fundamental concepts and definitions of commutative semigroup cohomology, including the notion of cocycles and homology theories. The authors then proceed to explore various approaches to the theory, such as the use of group actions, homological methods, and computational techniques.

Throughout the book, real-world examples and applications are used to illustrate the theoretical concepts and demonstrate their practical significance. These examples range from classical semigroups to more complex structures, such as Lie algebras and quantum groups. The authors also discuss the connections between commutative semigroup cohomology and other areas of mathematics, such as group representation theory, algebraic topology, and mathematical physics.

In conclusion, this book is a must-read for anyone interested in commutative semigroup cohomology and related fields. It provides a comprehensive and up-to-date introduction to the theory, compares and contrasts different approaches, and offers a wealth of computational methods and real-world applications. With its clear and accessible writing style, it is suitable for both advanced students and researchers seeking to deepen their understanding of this fascinating area of mathematics.

Weight: 314g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031082115
Edition number: 1st ed. 2022