Abstract
For an integer w, let 𝒮w be the algebraic triangulated category generated by a w-spherical object. We determine the Picard group of 𝒮w and show that each orbit category of 𝒮w is triangulated and is triangle equivalent to a certain orbit category of the bounded derived category of a standard tube. Moreover, we describe the Ringel–Hall Lie algebra associated to 𝒮w in the sense of Peng and Xiao.
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