Algebras and Representation Theory

• Κύριοι συγγραφείς: Erdmann, Karin (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut), Holm, Thorsten (http://id.loc.gov/vocabulary/relators/aut)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Springer Undergraduate Mathematics Series,
• Θέματα: Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Group theory.; Category theory (Mathematics).; Homological algebra.; Associative Rings and Algebras.; Commutative Rings and Algebras.; Group Theory and Generalizations.; Category Theory, Homological Algebra.

This carefully written textbook provides an accessible introduction to the representation theory of algebras, including representations of quivers. The book starts with basic topics on algebras and modules, covering fundamental results such as the Jordan-Hölder theorem on composition series, the Ar...

Πίνακας περιεχομένων:

• 1 Introduction
• 2 Algebras
• 3 Modules and Representations
• 4 Simple Modules in the Jordan-Hölder Theorem
• 5 Semisimple Modules and Semisimple Algebras
• 6 The Structure of Semisimple ALgebras - The Artin-Wedderburn Theorem
• 7 Semisimple Group Algebras and Maschke's Theorem
• 8 Indecomposable Modules
• 9 Representation Type
• 10 Representations of Quivers
• 11 Diagrams and Roots
• 12 Gabriel's Theorem
• 13 Proofs and Background
• 14 Appendix A: Induced Modules for Group Algebras
• 15 Appendix B: Solutions to Selected Exercises
• Index.