Basic Representation Theory of Algebras by Ibrahim Assem (Author)

Basic Representation Theory of Algebras
Authors: Ibrahim Assem, Flavio U. Coelho
Quality: Black White Pakistan Print

Introduction

Basic Representation Theory of Algebras by Ibrahim Assem and Flavio U. Coelho is a comprehensive text that explores the fundamental concepts of the representation theory of associative algebras. Part of the Graduate Texts in Mathematics series, the book provides a structured and rigorous introduction to the subject, targeting graduate students and researchers in mathematics. It begins with the foundational principles of module theory and progresses to more advanced topics, including quivers, path algebras, and almost split sequences. The authors emphasize the connection between algebraic structures and their representations, using clear proofs, examples, and exercises to reinforce understanding.

🏆 Key Features

✅ Foundational Coverage:

• Explains the basic concepts of representation theory, including modules, morphisms, and indecomposability.

• Develops the theory from elementary definitions to complex applications.

✅ Quiver and Path Algebra Theory:

• Introduces the theory of quivers and their representations.

• Explains path algebras and their role in module theory.

✅ Almost Split Sequences:

• Discusses almost split sequences and the Auslander-Reiten theory in detail.

• Provides insights into the classification of representations using this framework.

✅ Homological and Category Theory Connections:

• Explores the relationship between representation theory and homological algebra.

• Introduces triangulated categories and their relevance to module theory.

✅ Extensive Examples and Exercises:

• Includes numerous worked examples to clarify complex ideas.

• Offers exercises to reinforce understanding and encourage independent exploration.

🌟 Why This Book Is Essential

• Graduate-Level Focus: Tailored for graduate students and researchers.

• Balanced Approach: Combines theoretical depth with practical insights.

• Comprehensive Framework: Covers both classical and modern developments in the field.

• Rigorous and Accessible: Provides clear proofs and logical progression of ideas.

🎯 Conclusion

Basic Representation Theory of Algebras offers a structured and thorough exploration of algebraic representation theory. Its combination of foundational material, advanced topics, and practical examples makes it an invaluable resource for graduate students and researchers in algebra and related fields.