Modular classes of regular twisted Poisson structures on Lie algebroids

Abstract

We derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular classes of Lie algebras with a twisted triangular r-matrix. The special case of r-matrices associated to Frobenius Lie algebras is also studied.

13 pages, v.2 and 3: minor changes and two references added

References in corpus (1)

• The modular class of a twisted Poisson structure

Cited by in corpus (4)

• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• Twisted Rota-Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras
• On the geometric quantization of twisted Poisson manifolds
• Modular classes of Lie algebroid morphisms