Article ID Journal Published Year Pages File Type
4589496 Journal of Algebra 2006 17 Pages PDF
Abstract

To any unit form , qij∈Z, we associate a Lie algebra —an intersection matrix Lie algebra in the terminology of Slodowy—by means of generalized Serre relations. For a nonnegative unit form the isomorphism type of is determined by the equivalence class of q. Moreover for q nonnegative and connected with radical of rank zero or one respectively, the algebras turn out to be exactly the simply-laced Lie algebras which are finite-dimensional simple or affine Kac–Moody, respectively. In case q is connected, nonnegative of corank two and not of Dynkin type An, the algebra G(q) is elliptic.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory