Cluster Algebras in Higher Dimensions with Python (Golden Dawn Engineering)

Cluster Algebras in Higher Dimensions with Python (Golden Dawn Engineering)

Discover the fascinating world of Cluster Algebras with this comprehensive guide, covering topics from basic concepts to advanced applications. Whether you're a mathematician, physicist, or computer scientist, this book offers a rigorous yet accessible exploration of higher-dimensional cluster structures. With clear explanations and detailed examples, this book introduces you to the fundamental definitions and structures of cluster algebras. You'll learn about seed mutations, exchange relations, and the construction of higher-dimensional exchange matrices and quivers. The book also delves into the tropicalization of cluster algebras, the Laurent phenomenon, and the computation of cluster variables. As you progress through the chapters, you'll explore exciting topics such as cluster patterns and trees, periodicity in cluster algebras, quantum cluster algebras, and their representation in physics. You'll also discover the interplay between cluster algebras and algebraic combinatorics, homological methods, and topology. Key Features: - Comprehensive coverage of cluster algebra theory and applications in higher dimensions - Step-by-step explanations and detailed examples for clarity - Numerous algorithmic approaches for computational analysis By the end of this book, you'll have a deep understanding of the principles and techniques behind cluster algebras in higher dimensions and be equipped with the tools to apply this knowledge in your own research and work. Who This Book Is For: This book is suitable for mathematicians, physicists, and computer scientists interested in exploring the intricacies of cluster algebra theory in higher dimensions. It is also a valuable resource for graduate students and researchers looking to deepen their understanding and discover new applications in related fields such as representation theory, quantum mechanics, and optimization.