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math.QA2006
Hall algebras associated to triangulated categories
Jie Xiao, Fan Xu
By counting with triangles and the octohedral axiom, we find a direct way to prove the formula of Toën in \cite{Toen2005} for a triangulated category with (left) homological-finite…
math.QA2006★ 17 cited
Derived Categories and Lie Algebras
Jie Xiao, Fan Xu, Guanglian Zhang
Let $\md^b(A)$ be the derived category of a finite dimensional basic algebra with finite global dimension. We construct the Lie algebra arising from the 2-periodic version $\mk…
math.QA2006
Realizing Enveloping Algebras via Varieties of Modules
Ming Ding, Jie Xiao, Fan Xu
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra generated by indecomposable constructible sets in the varieties of modules for any…