A realization of elliptic Lie algebras of type by the Ringel–Hall approach

This article is to study relations between an elliptic Lie algebra g of type and the F-fixed point algebra AF of a tubular algebra A of type T(3,3,3) under a Frobenius morphism F. Using the explicit structure of the root category of the F-fixed point algebra AF, we prove that the elliptic Lie algebra g of type is isomorphic to the Ringel–Hall Lie algebra of the root category of the F-fixed point algebra AF.