Home > Papers

 
 
Cyclic complexes, Hall polynomials and simple Lie algebras
Chen Qinghua 1, Deng Bangming 2
1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875
2. Mathematical Sciences Center, Tsinghua University, Beijing 100084
*Correspondence author
#Submitted by
Subject:
Funding: 11331006) and Specialized Research Fund for the Doctoral Program of Higher Education（No.20110003110002）
Opened online: 6 November 2014
Accepted by: none
Citation: Chen Qinghua, Deng Bangming.Cyclic complexes, Hall polynomials and simple Lie algebras[OL]. [ 6 November 2014] http://en.paper.edu.cn/en_releasepaper/content/4615000
 
 
In this paper we study the category $C_m(scrP)$ of $m$-cycliccomplexes over $scrP$, where $scrP$ is the category of projectivemodules over a finite dimensional hereditary algebra $A$, and describe almost splitsequences in $C_m(scrP)$. This is applied to prove the existence of Hall polynomials in $C_m(scrP)$when $A$ is representation finite and $m ot=1$. We furtherintroduce the Hall algebra of $C_m(scrP)$ and its localization in the sense of Bridgeland.In the case when $A$ is representation finite, we use Hallpolynomials to define the generic Bridgeland--Hall algebra of $A$and show that it contains a subalgebra isomorphic to the integralform of the corresponding quantum enveloping algebra. This providesa construction of the simple Lie algebra associated with $A$.
Keywords:cyclic complex, Hall polynomial, quantum group, simple Lie algebra
 
 
 

For this paper
  • ● PDF (0B)
  • ● Revision 0 　　
  • ● Print this paper
  • ● Recommend this paper to a friend
  • ● Add to my favorite list

    Saved Papers

    Please enter a name for this paper to be shown in your personalized Saved Papers list

Tags
Add yours

Related Papers

Statistics
PDF Downloaded 81
Bookmarked 0
Recommend 5
Comments Array
Submit your papers