J. I. Hall, Michigan State University, East Lansing, MI
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Description
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