![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
ABSTRACT
The ℤ-grading determined by a long simple root of a rank n+1 affine Lie algebra over ℂ arises from a representation of a rank n semi-simple complex Lie algebra. Analysis of the relationship between the grading and the representation yields constructions that generalize the minuscule and adjoint algorithms as well as Kac’s construction of nontwisted affine Lie algebras.
Acknowledgment
Many thanks to J. M. Landsberg for suggesting the problem that led to this paper.