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What is A Tour of Representation Theory about?

Cover 1 Title page 4 Preface 12 Conventions 18 Part I . Algebras 20 Chapter 1. Representations of Algebras 22 1.1. Algebras 22 1.2. Representations 43 1.3. Primitive Ideals 60 1.4. Semisimplicity 69 1.5. Characters 84 Chapter 2. Further Topics on Algebras 98 2.1. Projectives 98 2.2. Frobenius and Symmetric Algebras 115 Part II . Groups 130 Chapter 3. Groups and Group Algebras 132 3.1. Generalities 132 3.2. First Examples 143 3.3. More Structure 150 3.4. Semisimple Group Algebras 162 3.5. Further Examples 169 3.6. Some Classical Theorems 178 3.7. Characters, Symmetric Polynomials, and Invariant Theory 189 3.8. Decomposing Tensor Powers 198 Chapter 4. Symmetric Groups 206 4.1. Gelfand-Zetlin Algebras 208 4.2. The Branching Graph 211 4.3. The Young Graph 216 4.4. Proof of the Graph Isomorphism Theorem 224 4.5. The Irreducible Representations 236 4.6. The Murnaghan-Nakayama Rule 241 4.7. Schur-Weyl Duality 254 Part III . Lie Algebras 262 Chapter 5. Lie Algebras and Enveloping Algebras 264 5.1. Lie Algebra Basics 265 5.2. Types of Lie Algebras 272 5.3. Three Theorems about Linear Lie Algebras 276 5.4. Enveloping Algebras 285 5.5. Generalities on Representations of Lie Algebras 297 5.6.

Author

Martin Lorenz

Language

EN