We show that every simple Lie algebra g of real rank at least two is isomorphic to a space of polynomials defined on the group N = exp n, where n is the nilpotent component of the Iwasawa decomposition of g. Using suitable coordinates on N, we then write a basis of this space of polynomials when g is split.
Ottazzi, A. (2010). Polynomial bases for split simple Lie algebras. PUBLICATIONES MATHEMATICAE, 76(1-2), 157-171.
Polynomial bases for split simple Lie algebras
OTTAZZI, ALESSANDRO
2010
Abstract
We show that every simple Lie algebra g of real rank at least two is isomorphic to a space of polynomials defined on the group N = exp n, where n is the nilpotent component of the Iwasawa decomposition of g. Using suitable coordinates on N, we then write a basis of this space of polynomials when g is split.
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