Let g = k ⊕ a ⊕ n be an Iwasawa decomposition for a simple real Lie algebra g. It is known that the subalgebra a ⊕ n determines g. In this paper we show how to construct g starting from the root system for the pair (g, a) whenever this root system is of type G2 . We use, in particular, Clifford algebra and the spin representation. We compute an explicit linear basis for the split, simple, real Lie algebra of type G2 and determine the structure constants.
A Clifford algebra approach to real rank one simple Lie algebras: The G_2 case
CIATTI, PAOLO
2002
Abstract
Let g = k ⊕ a ⊕ n be an Iwasawa decomposition for a simple real Lie algebra g. It is known that the subalgebra a ⊕ n determines g. In this paper we show how to construct g starting from the root system for the pair (g, a) whenever this root system is of type G2 . We use, in particular, Clifford algebra and the spin representation. We compute an explicit linear basis for the split, simple, real Lie algebra of type G2 and determine the structure constants.File in questo prodotto:
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