Results 1 to 10 of about 5,083 (123)
The twisted Drinfeld double of a finite group via gerbes and finite groupoids [PDF]
Algebraic & Geometric Topology, 2005 The twisted Drinfeld double (or quasi-quantum double) of a finite group with a 3-cocycle is identified with a certain twisted groupoid algebra. The groupoid is the loop (or inertia) groupoid of the original group and the twisting is shown geometrically ...
Altschüler +10 more
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Transitive Courant algebroids and double symplectic groupoids [PDF]
International Mathematics Research Notices, 2022 Abstract In this work, we extend the Lu–Weinstein construction of double symplectic groupoids to any Lie bialgebroid such that its associated Courant algebroid is transitive and its Atiyah algebroid integrable. We illustrate this result by showing how it generalises many of the examples of double symplectic groupoids that have appeared ...
Daniel Álvarez
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Coherent confluence modulo relations and double groupoids [PDF]
Journal of Pure and Applied Algebra, 2022 A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by confluence diagrams of critical branchings.
Benjamin Dupont, Philippe Malbos
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Double groupoids and homotopy 2-types [PDF]
Applied Categorical Structures, 2010 keywords: Double groupoid, classifying space, bisimplicial set, Kan complex, geometric realization, homotopy ...
Antonio M. Cegarra +2 more
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Double Bruhat cells and symplectic groupoids [PDF]
Transformation Groups, 2016 Let $G$ be a connected complex semisimple Lie group, equipped with a standard multiplicative Poisson structure $ _{\rm st}$ determined by a pair of opposite Borel subgroups $(B, B_-)$. We prove that for each $v$ in the Weyl group $W$ of $G$, the double Bruhat cell $G^{v,v} = BvB \cap B_-vB_-$ in $G$, together with the Poisson structure $ _{\rm st ...
Jiang-Hua Lu, Victor Mouquin
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From double Lie groupoids to local Lie 2-groupoids [PDF]
Bulletin of the Brazilian Mathematical Society, New Series, 2011 We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid.
A. Dold +17 more
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An algebraic framework for the Drinfeld double based on infinite groupoids [PDF]
Journal of Algebra, 2023 The Drinfeld double associated to the weak multiplier Hopf ($*$-) algebra pairing $\left\langle A, B\right\rangle$ is constructed. We show that the Drinfeld double is again a weak multiplier Hopf ($*$-) algebra. If $A$ and $B$ are algebraic quantum groupoids, then so does the double.
Nan Zhou, Shuanhong Wang
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FROM SYMPLECTIC GROUPOIDS TO DOUBLE STRUCTURES [PDF]
Geometric, Algebraic and Topological Methods for Quantum Field Theory, 2016 To appear in the proceedings of the School on \emph{Geometric, Algebraic and Topological Methods for Quantum Field Theory} in Villa de Leyva, Colombia, in July ...
Kirill C. H. Mackenzie
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Double groupoids and the symplectic category
Journal of Geometric Mechanics, 2018 We introduce the notion of a symplectic hopfoid, which is a "groupoid-like" object in the category of symplectic manifolds where morphisms are given by canonical relations. Such groupoid-like objects arise when applying a version of the cotangent functor to the structure maps of a Lie groupoid. We show that such objects are in one-to-one correspondence
Santiago Cañez
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The structure of double groupoids [PDF]
Journal of Pure and Applied Algebra, 2006 We give a general description of the structure of a discrete double groupoid (with an extra, quite natural, filling condition) in terms of groupoid factorizations and groupoid 2-cocycles with coefficients in abelian group bundles. Our description goes as follows: To any double groupoid, we associate an abelian group bundle and a second double groupoid,
Nicolás Andruskiewitsch, Sonia Natale
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