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Realizing enveloping algebras via varieties of modules

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Abstract

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. We also obtain Green’s formula 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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Authors and Affiliations

  1. Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China

    Ming Ding, Jie Xiao & Fan Xu

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  1. Ming Ding
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  2. Jie Xiao
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  3. Fan Xu
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Correspondence to Ming Ding.

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Dedicated to Professor J. A. Green on the occasion of his 80th birthday

Supported by NSF of China (Grant No. 10631010) and by NKBRPC (Grant No. 2006CB805905)

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Ding, M., Xiao, J. & Xu, F. Realizing enveloping algebras via varieties of modules. Acta. Math. Sin.-English Ser. 26, 29–48 (2010). https://doi.org/10.1007/s10114-010-9070-y

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  • DOI: https://doi.org/10.1007/s10114-010-9070-y

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