• ROOT MULTIPLICITIES FOR A CLASS OF QUASI AFFINE GENERALIZED KAC MOODY ALGEBRAS QAGGA2(1) OF RANK 4
Abstract
In this paper the concept of quasi affine generalized Kac Moody algebras (GKM) QAGGA2(1) are defined; the general form of connected Dynkin diagrams associated with this particular class of QAGGA2(1) are classified. Then, root multiplicities for some families of quasi affine generalized Kac Moody algebras are computed; First, we consider a general family QAGGA2(1) of symmetrizable Generalized Generalized Cartan Matrices (GGCM) of quasi affine type, with one imaginary simple root, of rank 4 which are obtained from the affine GCM A2(1) of rank 3. The real simple and imaginary simple roots for 3 different classes under this family QAGGA2(1) are explicitly computed; Finally the root multiplicities of all roots of GKM algebras QAGGA2(1) associated with these Borcherds Cartan matrices of order 4, which are obtained as extensions of the affine family A2(1) are then determined;
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