Quasi-Lie Bialgebroids and Twisted Poisson Manifolds

By Dmitry Roytenberg. 2001

162 citations recorded by the source corpus.

We develop a theory of quasi-Lie bialgebroids using a homological approach. This notion is a generalization of quasi-Lie bialgebras, as well as twisted Poisson structures with a 3-form background which have recently appeared in the context of string theory, and were studied by Ševera and Weinstein using a different method.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5695413fe5d8d0081913c4bf04cd74254723d495

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Citations in the corpus

Lie theory for nilpotent L∞-algebras (2004, background): “er [11].) More recently, there has been much interest in quasi-Poisson structures and Poisson-Nijenhuius 2 manifolds, where the associated dg Lie algebra is concentrated in degrees [−2,∞) (Roytenberg [19]). In this case, the associated formal deformation theory should be modelled by a 3-groupoid. It”
Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory (2003, background): “There is a notion of quasi-Gerstenhaber algebra (see [48]), and Bangoura has further proved that quasi-Batalin-Vilkovisky algebras give rise to quasi-Gerstenhaber algebras [6].”
Derived Brackets (2003, methodology): “Further properties of the Poisson structures with background and their gauge equivalence are studied in several recent articles, including [52], [49], [29] and [5].”
On weak Lie 2‐algebras (2007, background): “This example generalizes to any quasi-Lie bialgebroid [9].”
Universal lifting theorem and quasi-Poisson groupoids (2005, background): “The notion of quasi-Lie bialgebroids was first introduced by Roytenberg [23].”
AKSZ–BV Formalism and Courant Algebroid-Induced Topological Field Theories (2006, unknown): “Also, Hofman and Park [6][5] considered a generalization of the topological open membrane which takes values in a quasi-Lie bialgebroid [10], which is a Courant algebroid with a choice of a splitting.”
Membrane sigma-models and quantization of non-geometric flux backgrounds (2012, unknown): “The bracket on C is the skew-symmetrization of Roytenberg’s R-twisting of the Courant–Dorfman bracket given by [70, 34, 9] [ (Y1, α1) , (Y2, α2) ] R := ( [Y1, Y2]TM +R(α1, α2,−) , (2.”