Abstract
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 ( 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 .
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