Abstract
We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields X(M) on a dg-manifold M with homological vector field Q admits a structure of L∞[1]-algebra with the Lie derivative LQ as unary bracket λ1, and the Atiyah cocycle AtM corresponding to a torsion-free affine connection as binary bracket λ2.
Original language | English (US) |
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Pages (from-to) | 357-362 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 353 |
Issue number | 4 |
DOIs | |
State | Published - Apr 1 2015 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)