Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

Details Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I

2006-06-11

arxiv.org/abs/math/0606241v2

Mathematics

Rings and Algebras

Scientific paper

We develop geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. Geometric approach clarifies several questions, e.g. the notion of homological unit or A-infinity structure on A-infinity functors. We discuss Hochschild complexes of A-infinity algebras from geometric point of view. The paper contains homological versions of the notions of properness and smoothness of projective varieties as well as the non-commutative version of Hodge-to-de Rham degeneration conjecture. We also discuss a generalization of Deligne's conjecture which includes both Hochschild chains and cochains. We conclude the paper with the description of an action of the PROP of singular chains of the topological PROP of 2-dimensional surfaces on the Hochschild chain complex of an A-infinity algebra with the scalar product (this action is more or less equivalent to the structure of 2-dimensional Topological Field Theory associated with an "abstract" Calabi-Yau manifold).

Affiliated with

Also associated with

No associations

Rating

Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Notes on A-infinity algebras, A-infinity categories and non-commutative geometry. I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-528568