Jacobi algebroids and quasi Q-manifolds

2011/11/17 by Andrew James Bruce, Bruce, Andrew James
Mathematics · Medicine · Physics and Astronomy · #17B70 #53D10 #53D17 #58A50 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Ophthalmology and Eye Disorders #Symplectic Geometry (math.SG) #math-ph #math.DG #math.MP #math.SG #msc:17B70 #msc:53D10 #msc:53D17 #msc:58A50

paper · pdf · doi:10.48550/arxiv.1111.4044

14 pages. No major revision, further extra clarifying comments. Further comments and suggestions are very much welcomed

openalex publication_date 2011/11/17 · arxiv created 2011/12/03 · arxiv updated 2011/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We reformulate the notion of a Jacobi algebroid in terms of weighted odd Jacobi brackets. We then show how a Jacobi algebroid can be understood in terms of a kind of curved Q-manifold. In particular the homological condition on the odd vector field is deformed in a very specific way. This leads to the notion of a quasi Q-manifold.

Citations

• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics
• Odd Jacobi structures and classical BV-gauge systems

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