Semisimple Lie Algebras
Cartan subalgebras, root systems, and the Killing form.
Semisimple Lie Algebras. Cartan subalgebras, root systems, and the Killing form.
Foundations and canonical references
The standard treatments of semisimple lie algebras approach the subject from complementary angles. Humphreys, Introduction to Lie Algebras and Representation Theory (1972) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Cahn, Semi-Simple Lie Algebras and Their Representations (1984) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for semisimple lie algebras include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1972Introduction to Lie Algebras and Representation Theoryhumphreys-1972
- textbook · supporting · 1984Semi-Simple Lie Algebras and Their Representationscahn-1984
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