Realizing Enveloping Algebras via Varieties of Modules

Original · EN

By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(Λ) generated by indecomposable constructible sets in the varieties of modules for any finite dimensional C-algebra Λ. We obtain a geometric realization of the universal enveloping algebra R(Λ) of L(Λ). This generalizes the main result of Riedtmann in R. We also obtain Green's theorem in G in a geometric form for any finite dimensional C-algebra Λ and use it to give the comultiplication formula in R(Λ).