18. Semisimple Lie algebras and root systems

26 novembro 2020, 11:00 • Pedro Resende

More properties of the roots of semisimple Lie algebras: the only multiples of a root a that are roots are a and – a; the root spaces have dimension one. Weyl group of a semisimple algebra. Invariance of the set of roots under the action of the Weyl group. Root systems. The Weyl group of a root system. Direct sum of roots systems, irreducible root systems. General facts about angles between roots and root norms. Classification of the rank-two root systems. This lecture was based on sections 7.3–7.5 and 8.1–8.2 of Brian Hall's book.