Deformation of lie bialgebroid
WebThe Grothendieck–Teichmul¨ ler group acts via Lie ∞-automorphisms on the deformation complex of both Lie-quasi bialgebroids and quasi-Lie bialgebroids. Hence, the deformation quantization problem for Lie-quasi bialgebroids differs from its Lie bialgebroid counterpart and resembles more closely the one for Lie bialgebras, i.e., it belongs to
Deformation of lie bialgebroid
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WebFeb 1, 1998 · It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e.. the quantization problem, is posed. In particular, any regular triangular Lie bialgebroid is shown quantizable. For the Lie bialgebroid of a Poisson manifold, its quantization is equivalent to a star-product. Webbialgebroid was introduced as a geometric generalization of a left-symmetric bialgebra [2]. The double of a left-symmetric bialgebroid is not a left-symmetric algebroid anymore, but a pre-symplectic algebroid [27]. This result is parallel to the fact that the double of a Lie bialgebroid is a Courant algebroid [29].
WebBalavoine , Deformation of algebras over a quadratic operad, ... Courant algebroid and Lie bialgebroid contractions, J. Phys. A 37 (2004) 5189–5202 (English summary). ... Cohomology and deformations in graded Lie algebras, Bull. … WebIt is shown that a quantum groupoid (or a QUE algebroid, i.e., deformation of the universal enveloping algebra of a Lie algebroid) naturally gives rise to a Lie bialgebroid as a …
WebAug 1, 2024 · This result is parallel to the fact that the double of a Lie bialgebroid, 1 is not a Lie algebroid, but a Courant algebroid . Furthermore, if we consider the commutator of a left-symmetric bialgebroid, we obtain a matched pair of Lie algebroids, whose double is the symplectic Lie algebroid associated to the pre-symplectic algebroid. WebApr 17, 2010 · In this paper, the structure of higher nonabelian omni-Lie algebroid is studied. The concept of higher nonabelian omni-Lie algebras on direct sum bundle DE⊕∧nJE is introduced, and its related ...
WebAug 19, 1997 · It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the quantization problem, is posed. In particular, any regular triangular Lie bialgebroid is shown quantizable. For the Lie bialgebroid of a Poisson manifold, its quantization is equivalent to a star-product.
WebDec 16, 2015 · This shows also that by contrast to the even case the properad governing odd Lie bialgebras admits precisely one non-trivial automorphism - the standard … bottom boat cleaning near meWebFeb 15, 2024 · By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid from a 2-term (Formula presented.)-algebra, which is proposed to be the ... bottom boat paintWebApr 17, 2010 · We introduce and study a special type of deformation called by unfoldings of Lie algebroids which generalizes the theory due to Suwa for singular … hay round balerWebA Note on Multi-Oriented Graph Complexes and Deformation Quantization of Lie Bialgebroids Morand, Kevin Universal solutions to deformation quantization problems … bottom boat paint colorsA Lie bialgebroid is a mathematical structure in the area of non-Riemannian differential geometry. In brief a Lie bialgebroid are two compatible Lie algebroids defined on dual vector bundles. They form the vector bundle version of a Lie bialgebra. See more Preliminary notions Remember that a Lie algebroid is defined as a skew-symmetric operation [.,.] on the sections Γ(A) of a vector bundle A→M over a smooth manifold M together with a vector bundle … See more It is well known that the infinitesimal version of a Lie groupoid is a Lie algebroid. (As a special case the infinitesimal version of a See more 1. A Lie bialgebra are two Lie algebras (g,[.,.]g) and (g ,[.,.]*) on dual vector spaces g and g such that the Chevalley–Eilenberg differential δ* is a derivation of the g-bracket. 2. A Poisson manifold (M,π) gives naturally rise to a Lie … See more For Lie bialgebras (g,g ) there is the notion of Manin triples, i.e. c=g+g can be endowed with the structure of a Lie algebra such that g and g are subalgebras and c contains the representation of g on g , vice versa. The sum structure is just See more hay royds collieryWebthe Lie bialgebroid (A,A ∗). The Courant algebroid structure on A⊕A originally proposed by Liu et al. [11] as a “Drinfeld double” of (A,A∗) is recovered from the homological double by Kosmann-Schwarzbach’s derived bracket construction [8]. This generalizes the homological approach to Lie bialgebras pioneered by Lecomte bottom boat painting near meWebFeb 1, 2007 · On L we have given the structure of a quasi-Lie bialgebroid. Remark 3.13. If in addition {μ, ϕ} R = 0 is satisfied then (L, L ∗) is a Lie bialgebroid [21]. But only if ϕ = 0 the space of sections Γ ∞ (L ∗) is closed under the Courant bracket and L ∗ is a Dirac structure. hay round bale price