nLab
curved dg-algebra

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Idea

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 =F \nabla \circ \nabla = F_\nabla, where F F_\nabla is the curvature 2-form of the connection (valued, here, in fiber endomorphism)s.

Curved dg-algebras appear in the description of various TQFTs.

(…)

References

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 (82.113.106.172)