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Related papers: Lie algebroids, Lie groupoids and TFT

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In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…

Quantum Algebra · Mathematics 2009-07-16 Nikolai Neumaier , Stefan Waldmann

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different…

High Energy Physics - Theory · Physics 2007-05-23 L. Snobl

Partial Isometries are important constructs that help give nontrivial solutions once a simple solution is known. We generalize this notion to Extended Partial Isometries and include operators which have right inverses but no left inverses…

High Energy Physics - Theory · Physics 2007-05-23 Tewodros Amdeberhan , Arvind Ayyer

In this work we study B-field transformations of multiplicative Poisson bivectors on a Lie groupoid G. We are concerned with B-fields given by multiplicative closed 2-forms on G. We view Poisson groupoids and their B-field symmetries as…

Symplectic Geometry · Mathematics 2011-09-01 Cristian Ortiz

In the present paper we describe a new class of Gelfand--Tsetlin modules for an arbitrary complex simple finite-dimensional Lie algebra g and give their geometric realization as the space of delta-functions" on the flag manifold G/B…

Representation Theory · Mathematics 2018-11-28 Vyacheslav Futorny , Libor Krizka

In this paper we present the solution to a longstanding problem of differential geometry: Lie's third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we…

Differential Geometry · Mathematics 2007-05-23 Marius Crainic , Rui L. Fernandes

In this paper we show how connections and their generalizations on transitive Lie algebroids are related to the notion of connections in the framework of the derivation-based noncommutative geometry. In order to compare the two…

Differential Geometry · Mathematics 2011-11-28 Serge Lazzarini , Thierry Masson

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…

High Energy Physics - Theory · Physics 2009-10-31 P. Bantay

This manuscript is devoted to introduce a gauge theory of the Lorentz Group based on the ambiguity emerging in dealing with isometric diffeo-morphism-induced Lorentz transformations. The behaviors under local transformations of fermion…

General Relativity and Quantum Cosmology · Physics 2014-11-18 Nakia Carlevaro , Orchidea Maria Lecian , Giovanni Montani

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

High Energy Physics - Theory · Physics 2008-02-03 C. De Concini , Victor G. Kac , C. Procesi

We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we…

Mathematical Physics · Physics 2018-08-13 Samuel Monnier

For massive and conformal quantum field theories in 1+1 dimensions with a global gauge group we consider soliton automorphisms, viz. automorphisms of the quasilocal algebra which act like two different global symmetry transformations on the…

High Energy Physics - Theory · Physics 2015-06-26 Michael Mueger

A noncommutative space is considered the position operators of which satisfy the commutativity relations of a Lie algebra. The basic tools for calculation on this space, including the product of the fields, inner product and the proper…

High Energy Physics - Theory · Physics 2008-11-26 A. H. Fatollahi , M. Khorrami

In this paper we discuss some connections between groupoids and Frobenius algebras specialized in the case of Poisson sigma models with boundary. We prove a correspondence between groupoids in the category Set and relative Frobenius…

Mathematical Physics · Physics 2015-09-14 Ivan Contreras

Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the…

Differential Geometry · Mathematics 2016-09-07 K. Grabowska , J. Grabowski , P. Urbanski

Projective structures on topological surfaces support the structure of 2d CFTs with a degree of technical simplification. We propose a complex analytic space $\mathcal{P}_g$ biholomorphic to $T^*_{(1,0)} \mathcal{M}_g$ as a candidate moduli…

High Energy Physics - Theory · Physics 2024-11-05 Xiao Liu

We study the behavior of the modular class of a Lie algebroid under general Lie algebroid morphisms by introducing the relative modular class. We investigate the modular classes of pull-back morphisms and of base-preserving morphisms…

Differential Geometry · Mathematics 2008-04-18 Yvette Kosmann-Schwarzbach , Camille Laurent-Gengoux , Alan Weinstein

We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag…

Quantum Algebra · Mathematics 2025-10-15 Mao Hoshino

There is the notion of action Lie algebroids, containing information about Lie algebras and their actions, which is why it is natural to generalise gauge theories to a formulation using Lie algebroids; these allow structure functions in…

Mathematical Physics · Physics 2021-10-01 Simon-Raphael Fischer

We extend the algebra of local observables in topological conformal field theories by nonlocal operators. This allows to construct parameter-dependent operations realized via certain integrals over the compactified moduli spaces, satisfying…

Quantum Algebra · Mathematics 2021-09-28 Anton M. Zeitlin