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· 제목 : Introduction to Lie Algebras : Finite and Infinite Dimension (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 대수학 일반
· ISBN : 9781470479152
· 쪽수 : 514쪽
· 출판일 : 2025-02-28
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 대수학 > 대수학 일반
· ISBN : 9781470479152
· 쪽수 : 514쪽
· 출판일 : 2025-02-28
목차
- Part I. Preliminaries
- Algebras
- Examples of Lie algebras
- Lie groups
- Part II. Classification
- Lie algebra basics
- The Cartan decomposition
- Semisimple Lie algebras: Basic structure
- Classification of root systems
- Semisimple Lie algebras: Classification
- Part III. Important constructions
- Finite degree representations of $\mathfrak{sl}_2(\mathbb{K})$
- PBW and free Lie algebras
- Casimir operators and Weyl's Theorem II
- Chevalley bases and integration
- Kac-Moody Lie algebras
- Part IV. Representation
- Integrable representations
- The spherical case and Serre's Theorem
- Irreducible weight modules for $\mathfrak{sl}_2(\mathbb{K})$
- Part V. Infinite dimension
- Some infinite-dimensional Lie algebras
- Triangular decomposition and category $\mathcal{O}$
- Character theory
- Representation of the Virasoro algebra
- Part VI. Appendices
- Appendix A. Algebra basics
- Appendix B. Bilinear forms
- Appendix C. Finite groups generated by reflections
- Bibliography
- Index
