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From quantum groups to Liouville and dilaton quantum gravity
Journal of High Energy Physics, 2022 We investigate the underlying quantum group symmetry of 2d Liouville and dilaton gravity models, both consolidating known results and extending them to the cases with N $$ \mathcal{N} $$ = 1 supersymmetry.
Yale Fan, Thomas G. Mertens
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From Quantum Automorphism of (Directed) Graphs to the Associated Multiplier Hopf Algebras
Mathematics, 2023 This is a noticeably short biography and introductory paper on multiplier Hopf algebras. It delves into questions regarding the significance of this abstract construction and the motivation behind its creation.
Farrokh Razavinia +1 more
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Exchange dynamical quantum groups [PDF]
, 1999 For any simple Lie algebra g and any complex number q which is not zero or a nontrivial root of unity, we construct a dynamical quantum group (Hopf algebroid), whose representation theory is essentially the same as the representation theory of the ...
Etingof, Pavel, Varchenko, Alexander
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Frobenius–Schur Indicator for Categories with Duality
Axioms, 2012 We introduce the Frobenius–Schur indicator for categories with duality to give a category-theoretical understanding of various generalizations of the Frobenius–Schur theorem including that for semisimple quasi-Hopf algebras, weak Hopf C*-algebras and ...
Kenichi Shimizu
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Polyadic Hopf Algebras and Quantum Groups
East European Journal of Physics, 2021 This article continues the study of concrete algebra-like structures in our polyadic approach, where the arities of all operations are initially taken as arbitrary, but the relations between them, the arity shapes, are to be found from some natural ...
S. Duplij
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Quantum reference frames for general symmetry groups [PDF]
Quantum, 2020 A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described.
Anne-Catherine de la Hamette +1 more
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Quantum Groups, Coherent States, Squeezing and Lattice Quantum Mechanics [PDF]
, 1993 By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite difference operators.
Celeghini +4 more
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Journal of Algebra, 2001 An entwining structure [\textit{T. Brzeziński} and \textit{S. Majid}, Commun. Math. Phys. 191, No. 2, 467-492 (1998; Zbl 0899.55016)] comprises an algebra \(A\), a coalgebra \(C\) and a linear map \(\psi\colon C\otimes A\to A\otimes C\), which is compatible with the multiplication and unit of \(A\), and the comultiplication and counit of \(C ...
Hobst, Daniela, Pareigis, Bodo
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Cyclicity for categorified quantum groups [PDF]
, 2015 We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morphisms f. This is accomplished via a modified diagrammatic formalism.Comment:
Beliakova, Anna +3 more
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Quantum group and quantum symmetry [PDF]
Physics Reports, 1995 This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation.
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