77 research outputs found
The Ringel--Hall Lie algebra of a spherical object
For an integer , let \cs_w be the algebraic triangulated category
generated by a -spherical object. We determine the Picard group of \cs_w
and show that each orbit category of \cs_w is triangulated and is triangle
equivalent to a certain orbit category of the bounded derived category of a
standard tube. When , the orbit category \cs_w/\Sigma^2 is 2-periodic
triangulated, and we characterize the associated Ringel--Hall Lie algebra in
the sense of Peng and Xiao.Comment: 26page
Exchange graphs of cluster algebras have the non-leaving-face property
The claim in the title is proved
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