In this paper we classiy real simple Lie algebras with reduced root system, i.e. the algebras with a root system belonging to one of the families Ar , Br , Cr , Dr (r ∈ N), Er (r = 6, 7, 8), F4 , G2 . We use the tools of Clifford algebra classification, and derive the formulae for the root multiplicities. For the classical cases we indicate explicit models of matrix algebras with the derived root multiplicities.
A Clifford algebra approach to real simple Lie algebras, I: The algebras with reduced root system
CIATTI, PAOLO
2002
Abstract
In this paper we classiy real simple Lie algebras with reduced root system, i.e. the algebras with a root system belonging to one of the families Ar , Br , Cr , Dr (r ∈ N), Er (r = 6, 7, 8), F4 , G2 . We use the tools of Clifford algebra classification, and derive the formulae for the root multiplicities. For the classical cases we indicate explicit models of matrix algebras with the derived root multiplicities.
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