A realization of elliptic Lie algebras of type F_4~((2,2)) by the Ringel-Hall approach

摘要

This article is to study relations between an elliptic Lie algebra g of type F_4~((2,2)) and the F-fixed point algebra A~F of a tubular algebra A of type T{double-struck}(3,3,3) under a Frobenius morphism F. Using the explicit structure of the root category of the F-fixed point algebra A~F, we prove that the elliptic Lie algebra g of type F_4~((2,2)) is isomorphic to the Ringel-Hall Lie algebra of the root category of the F-fixed point algebra A~F.