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Related papers: Duality for action bialgebroids

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We extend the notion of Lie bialgebroids for more general bracket structures used in string and M theories. We formalize the notions of calculus and dual calculi on algebroids. We achieve this by reinterpreting the main results of the…

High Energy Physics - Theory · Physics 2023-12-12 Aybike Çatal-Özer , Keremcan Doğan , Cem Yetişmişoğlu

For a Hopf algebra B with bijective antipode, we show that the Heisenberg double H(B^*) is a braided commutative Yetter--Drinfeld module algebra over the Drinfeld double D(B). The braiding structure allows generalizing H(B^*) =…

Quantum Algebra · Mathematics 2009-10-15 A. M. Semikhatov

Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…

High Energy Physics - Theory · Physics 2024-03-19 G. B. de Gracia , B. M. Pimentel

This work explores the geometrical/algebraic framework of Lie algebroids, with a specific focus on the decoupling and coupling phenomena within the bicocycle double cross product realization. The bicocycle double cross product theory serves…

Differential Geometry · Mathematics 2025-03-18 Begüm Ateşli , Oğul Esen , Serkan Sütlü

Dualities play a central role in the study of quantum spin chains, providing insight into the structure of quantum phase diagrams and phase transitions. In this work we study categorical dualities, which are defined as bounded-spread…

Mathematical Physics · Physics 2026-03-26 Corey Jones , Kylan Schatz , Dominic J. Williamson

We extend a quantized skew Howe duality result for Type $\mathbf{A}$ algebras to orthogonal types via a seesaw. We develop an operator commutant version of the First Fundamental Theorem of invariant theory for $U_q(\mathfrak{so}_n)$ using a…

Quantum Algebra · Mathematics 2022-08-23 Willie Aboumrad

Commuting pairs of algebraic structures on a set have been studied by several authors and may be described equivalently as algebras for the tensor product of Lawvere theories, or more basically as certain bifunctors that here we call bifold…

Category Theory · Mathematics 2022-05-20 Rory B. B. Lucyshyn-Wright

Let H be a bialgebra and D an H-bimodule algebra H-bicomodule coalgebra. We find sufficient conditions on D for the L-R-smash product algebra and coalgebra structures on D\otimes H to form a bialgebra (in this case we say that (H, D) is an…

Quantum Algebra · Mathematics 2008-05-23 Florin Panaite , Freddy Van Oystaeyen

Studying two-dimensional field theories in the presence of defect lines naturally gives rise to monoidal categories: their objects are the different (topological) defect conditions, their morphisms are junction fields, and their tensor…

High Energy Physics - Theory · Physics 2012-02-09 Nils Carqueville , Ingo Runkel

We find that in "two-photon"-like processes in the scalar $\varphi^3_E$ model and also in hadron-pair production arising from the collisions of a real (transversely polarized) and a highly virtual, longitudinally polarized, photon in QCD,…

High Energy Physics - Phenomenology · Physics 2008-11-27 I. V. Anikin , I. O. Cherednikov , N. G. Stefanis , O. V. Teryaev

The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a…

High Energy Physics - Theory · Physics 2009-11-11 D. Dalmazi , Elias L. Mendonca

We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…

Probability · Mathematics 2018-08-01 Frank Redig , Federico Sau

We provide a full realization of the electromagnetic duality at the boundary by extending the phase space of Maxwell's theory through the introduction of edge modes and their conjugate momenta. We show how such extension, which follows from…

High Energy Physics - Theory · Physics 2018-12-24 Laurent Freidel , Daniele Pranzetti

Dualities are often supposed to be foundational, but they may come into conflict with background independence, because a hidden fixed structures is needed to define the duality transformation. This conflict can be eliminated by extending a…

High Energy Physics - Theory · Physics 2016-12-21 Lee Smolin

In this work we investigate the notion of action or coaction of a finite quantum groupoid in von Neumann algebras context. In particular we prove a double crossed product theorem and prove the existence of an universal von Neumann algebra…

Quantum Algebra · Mathematics 2007-05-23 Jean-Michel Vallin

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…

Operator Algebras · Mathematics 2024-06-25 Jyotishman Bhowmick , Arnab Mandal , Sutanu Roy , Adam Skalski

We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the action of the group GL(m). The algebra is generated by right…

Quantum Algebra · Mathematics 2015-03-17 D. Gurevich , P. Pyatov , P. Saponov

We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin…

Mathematical Physics · Physics 2016-02-22 M. Beketov , A. Liashyk , A. Zabrodin , A. Zotov

We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…

High Energy Physics - Theory · Physics 2009-10-28 Jonathan Beck

Using examples of a D=2 chiral scalar and a duality-symmetric formulation of D=4 Maxwell theory we study duality properties of actions for describing chiral bosons. In particular, in the D=4 case, upon performing a duality transform of an…

High Energy Physics - Theory · Physics 2009-10-31 Alexey Maznytsia , Christian Preitschopf , Dmitri Sorokin