The primary reference on this topic is the classic text " Lie Algebras
if np.all(unique_off_diag >= -1): # Could be A, D, or E # Differentiate based on graph connectivity (simplified here) algebra_type = "Simply Laced (Type A, D, or E)" else: # Contains -2 or -3 if -3 in unique_off_diag: algebra_type = "Type G2" elif -2 in unique_off_diag: # Check for B_n vs C_n symmetry properties usually requires deeper analysis algebra_type = "Non-Simply Laced (Type B, C, or F)" Args: matrix (list of lists or np.array): An n x n integer matrix.