Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589496 | Journal of Algebra | 2006 | 17 Pages |
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.
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