On root categories of finite-dimenisonal algebras

Details On root categories of finite-dimenisonal algebras On root categories of finite-dimenisonal algebras

2011-03-17

arxiv.org/abs/1103.3335v1

Mathematics

Representation Theory

25 pages

Scientific paper

For any finite-dimensional algebra $A$ over a field $k$ with finite global dimension, we investigate the root category $\cR_A$ as the triangulated hull of the 2-periodic orbit category of $A$ via the construction of B. Keller in "On triangulated orbit categories". This is motivated by Ringel-Hall Lie algebras associated to 2-periodic triangulated categories. As an application, we study the Ringel-Hall Lie algebras for a class of finite-dimensional $k$-algebras with global dimension 2, which turn out to give an alternative answer for a question of GIM Lie algebras by Slodowy in "Beyond Kac-Moody algebra, and inside".

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