Vertex algebras generated by Lie algebras

In this paper we introduce a notion of vertex Lie algebra U, in a way a "half" of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset of V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex algebra V a given homomorphism from U to V of vertex Lie algebras extends uniquely to a homomorphism from V(U) to V of vertex algebras. In the second part of paper we study under what conditions on structure constants one can construct a vertex Lie algebra U by starting with a given commutator formula for fields.Comment: 38 pages, LaTe

Explicit solutions to fractional diffusion equations via Generalized Gamma Convolution

In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional diffusion equations involving the adjoint operators of a square Bessel process and a Bessel process