‎In this paper‎, ‎using fixed point method‎, ‎we prove the generalized Hyers-Ulam stability of‎ ‎random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras‎ ‎and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

This paper is a sequel to the paper [7] in which generalized Cartan type S Lie algebras tzS(A, T, φ) over a field F of characteristic 0 were studied. We have tried to make this paper independent of other papers. So in Section 2, we give a description of relevant Lie algebras and some basic facts which will be used in this paper. In Section 3 we introduce a class of Lie algebras which are subalg...

The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G2 i ↪→ so(7), and generalized conformal so(7)-Verma modules of scalar type. As a result, we classify t...