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noncommutative thin scheme

Given a commutative field kk, a noncommutative thin kk-scheme (in the terminology of Maxim Kontsevich) is a left exact functor from the category Alg k fdAlg^{fd}_k of finite dimensional kk-algebras to Set, or equivalently by duality, from Coalg k fdopCoalg^{fd}_k^{op} to SetSet. Every such functor is representable by a kk-coalgebra.

  • L. le Bruyn, Noncommutative geometry and dual coalgebras, arXiv:0805.2377

  • M. Kontsevich, Y. Soibelman, Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, math.RA/0606241

  • blog entry

Revised on March 6, 2013 19:24:22 by Zoran Škoda (161.53.130.104)