Realizing Enveloping Algebras via Varieties of Modules
نویسندگان
چکیده
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 Calgebra Λ. We obtain a geometric realization of the universal enveloping algebra R(Λ) of L(Λ). This generalizes the main result of Riedtmann in [19]. We also obtain Green’s theorem in [6] in a geometric form for any finite dimensional C-algebra Λ and use it to give the comultiplication formula in R(Λ).
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