From triangulated categories to Lie algebras: A theorem of Peng and Xiao

By Andrew Hubery. 2005

63 citations recorded by the source corpus.

We present a simplified and more intuitive proof of a theorem of Peng and Xiao, which constructs a Lie algebra from any 2-periodic triangulated k-category (satisfying some finiteness assumptions).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fae8cfca217bea5eb7fdf2b62396518f5607aba4

Citations in the corpus

• On differential graded categories (2006, unknown): “ever, if one tries to mimick the construction of H(A) for a triangulated category Tby replacing short exact sequences by triangles one obtains a multiplication which fails to be associative, cf. [70] [68]. It is remarkable that nevertheless, as shown by Peng-Xiao [115] [116] [117], the commutator as”