Mathematics – K-Theory and Homology
Scientific paper
2007-07-17
Mathematics
K-Theory and Homology
24 pages
Scientific paper
A notion of Hochschild cohomology of an abelian category was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism from the Hochschild cohomology into the graded centre of the (bounded) derived category. An element in the second Hochschild cohomology group corresponds to a first order deformation of the abelian category (Lowen and Van den Bergh, 2006). The problem of deforming single objects of the bounded derived category was treated by Lowen (2005). In this paper we show that the image of the Hochschild cohomology element under the characteristic morphism encodes precisely the obstructions to deforming single objects of the bounded derived category. Hence this paper provides a missing link between the above works. Finally we discuss some implications of these facts in the direction of a ``derived deformation theory''.
No associations
LandOfFree
Hochschild cohomology, the characteristic morphism and derived deformations 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 Hochschild cohomology, the characteristic morphism and derived deformations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hochschild cohomology, the characteristic morphism and derived deformations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-552855