Triangulated categories and Kac-Moody algebras

By using the Ringel-Hall algebra approach, we find a Lie algebra arising in each triangulated category with T ^sup 2^=1, where T is the translation functor. In particular, the generic form of the Lie algebras determined by the root categories, the 2-period orbit categories of the derived categories...

Full description

Saved in:
Bibliographic Details
Published in:Inventiones mathematicae 2000-06, Vol.140 (3), p.563-603
Main Authors: Peng, Liangang, Xiao, Jie
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By using the Ringel-Hall algebra approach, we find a Lie algebra arising in each triangulated category with T ^sup 2^=1, where T is the translation functor. In particular, the generic form of the Lie algebras determined by the root categories, the 2-period orbit categories of the derived categories of finite dimensional hereditary associative algebras, gives a realization of all symmetrizable Kac-Moody Lie algebras.[PUBLICATION ABSTRACT]
ISSN:0020-9910
1432-1297
DOI:10.1007/s002220000062