A curved dg-algebra is like a dg-algebra, but instead of the differential squaring to 0, it squares to the graded commutator with a fixed element of the algebra: its “curvature”.
This is like the covariant derivative on the sections of a vector bundle with connection satisfying , where is the curvature 2-form of the connection (valued, here, in fiber endomorphism)s.
Curved dg-algebras appear in the description of various TQFTs.
A basic exposition of the definition is in
- A. Polishchuk, Introduction to curved dg-algebra , notes taken in a talk (pdf)
For applications in derived categories of D-branes in Landau-Ginzburg models see
An natural construction of curved dg-algebras as de Rham / Dolbeault complexes on a circle 2-bundle with connection is in
- Jonathan Block, Duality and equivalence of module categories in noncommutative geometry, pdf, in R. Bott Memorial Volume
and with more details in section 2 of
Revised on April 20, 2012 22:51:03
by Urs Schreiber