Realizing Enveloping Algebras via Varieties of Modules  

作　　者：Ming DING Jie XIAO Fan XU 

机构地区：[1]Department of Mathematics, Tsinghua University, Beijing 100084~ P. R~ China

出　　处：《Acta Mathematica Sinica,English Series》2010年第1期29-48,共20页数学学报（英文版）

基　　金：Supported by NSF of China (Grant No. 10631010);by NKBRPC (Grant No. 2006CB805905)

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

关 键 词：Ringel-Hall algebra constructible set VARIETY universal enveloping algebra 

分 类 号：O152.5[理学—数学] TP311.13[理学—基础数学]