Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory

Kosmann–Schwarzbach, Yvette

doi:10.1007/0-8176-4419-9_12

Cited by 56 publications

(62 citation statements)

References 48 publications

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“…, ranging from 1 to 2d. An arbitrary generalized vector is written as 54) namely the index I splits into upper and lower indices according to…”

Section: The Induced Courant Algebroidmentioning

confidence: 99%

Sigma models for genuinely non-geometric backgrounds

Jonke¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.1 thanasis@itp.uni-hannover.de 2

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“…, ranging from 1 to 2d. An arbitrary generalized vector is written as 54) namely the index I splits into upper and lower indices according to…”

Section: The Induced Courant Algebroidmentioning

confidence: 99%

Sigma models for genuinely non-geometric backgrounds

Jonke¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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“…The aim of this note is to construct the theory of twisting on associative algebras according to the philosophy and construction in [12] and [21]. At first, we will define a twisting operation in the category of associative algebras.…”

Section: Or Classical Yang-baxter Equation)mentioning

confidence: 99%

“…The twisting operations provide a method of analyzing Manin triples. In the context of Poisson geometry, they gave a detailed study of twisting operations (see Kosmann-Schwarzbach [10], [12] and Roytenberg [21], [22]). We briefly describe twisting operations.…”

Section: Introductionmentioning

confidence: 99%

Twisting on associative algebras and Rota–Baxter type operators

Uchino¹

2010

J. Noncommut. Geom.

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Abstract. We introduce an operation called "twisting" on the Hochschild complex by analogy with Drinfeld's twisting operations. By using the twisting and derived bracket constructions, we study differential graded Lie algebra structures associated to the bi-graded Hochschild complex. We show that Rota-Baxter type operators are solutions of Maurer-Cartan equations. As an application of twisting, we give a construction of associative Nijenhuis operators. (2010). 13D03, 16S80, 17B62. Mathematics Subject Classification

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“…It can de deduced from a theorem of Chevalley [21] that the graph of π is the annihilator of the pure spinor λ (π) . Thus, in the spinor approach to Poisson and twisted Poisson structures, the inhomogeneous form λ (π) is viewed as a pure spinor defining the graph of π. called the Courant bracket with background ψ, or the ψ-twisted Courant bracket (see [111,69,70] and, for further developments, [115,71]). A Lagrangian sub-bundle of a Courant algebroid whose sections are closed under the Courant bracket is called a Dirac structure.…”

Section: Pure Spinorsmentioning

confidence: 99%