Root Multiplicity of a Special Generalized Kac-Moody Algebra EB2

摘要

The author systematically introduces the closed root multiplicity of a special generalized Kac-Moody algebra which was extended from the finite Kac-Moody algebra .The representative theory is one of the issues of current research in generalized Kac-Moody algebra. The author firstly introduces the basic concepts of the representative theory in detail. Then the multiplicity formula for closed root is popularized from EA2 to EB2. Only through the application of non-homogeneous linear equations can solve the complex calculation of root multiplicity. And then obtain its general solution about the multiplicity of the root for the generalized Kac-Moody algebra EB2. This method has wide applications in other fields.