Batalin-Vilkovisky Structures on Ext and Tor

Details Batalin-Vilkovisky Structures on Ext and Tor Batalin-Vilkovisky Structures on Ext and Tor

2012-03-22

arxiv.org/abs/1203.4984v1

Mathematics

K-Theory and Homology

49 pages

Scientific paper

This article studies the algebraic structure of homology theories defined by a left Hopf algebroid U over a possibly noncommutative base algebra A, such as for example Hochschild, Lie algebroid (in particular Lie algebra and Poisson), or group and etale groupoid (co)homology. Explicit formulae for the canonical Gerstenhaber algebra structure on Ext_U(A,A) are given. The main technical result constructs a Lie derivative satisfying a generalised Cartan-Rinehart homotopy formula whose essence is that Tor^U(M,A) becomes for suitable right U-modules M a Batalin-Vilkovisky module over Ext_U(A,A), or in the words of Nest, Tamarkin, Tsygan and others, that Ext_U(A,A) and Tor^U(M,A) form a differential calculus. As an illustration, we show how the well-known operators from differential geometry in the classical Cartan homotopy formula can be obtained. Another application consists in generalising Ginzburg's result that the cohomology ring of a Calabi-Yau algebra is a Batalin-Vilkovisky algebra to twisted Calabi-Yau algebras.

Affiliated with

Also associated with

No associations

Rating

Batalin-Vilkovisky Structures on Ext and Tor 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 Batalin-Vilkovisky Structures on Ext and Tor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Batalin-Vilkovisky Structures on Ext and Tor will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-381810