Results 1 to 10 of about 22,579,506 (332)
Introduction to Quantum Groups [PDF]
Reviews in Mathematical Physics, 1997 We give an elementary introduction to the theory of algebraic and topological quantum groups (in the spirit of S. L. Woronowicz). In particular, we recall the basic facts from Hopf (*-) algebra theory, theory of compact (matrix) quantum groups and the ...
P. Podlés, E. Müller
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Quantum groups and Yang-Baxter equations
Natural Science ReviewThis introductory review is devoted to the newest section of the theory of symmetries -- the theory of quantum groups. The principles of the theory of quantum groups are reviewed from the point of view of the possibility of their use for deformations ...
A. P. Isaev
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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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K-theoretic Hall algebras, quantum groups and super quantum groups [PDF]
Selecta Mathematica, 2020 We prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum group.
M. Varagnolo, E. Vasserot
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Solutions by Quadratures of Complex Bernoulli Differential Equations and Their Quantum Deformation
Axioms, 2023 It is shown that the complex Bernoulli differential equations admitting the supplementary structure of a Lie–Hamilton system related to the book algebra b2 can always be solved by quadratures, providing an explicit solution of the equations. In addition,
Rutwig Campoamor-Stursberg +2 more
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A representation-theoretic proof of the branching rule for Macdonald polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of $U_q(gl_n)$. In the Gelfand-Tsetlin basis, we show that diagonal
Yi Sun
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Log-Modular Quantum Groups at Even Roots of Unity and the Quantum Frobenius I [PDF]
Communications in Mathematical Physics, 2018 We construct log-modular quantum groups at even order roots of unity, both as finite-dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de-equivariantization procedure.
C. Negron
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Non-Archimedean quantum mechanics via quantum groups
Nuclear Physics B, 2022 We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of arbitrary ...
W.A. Zúñiga-Galindo
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Categorically Morita Equivalent Compact Quantum Groups [PDF]
Documenta Mathematica, 2017 We give a dynamical characterization of categorical Morita equivalence between compact quantum groups. More precisely, by a Tannaka-Krein type duality, a unital C*-algebra endowed with commuting actions of two compact quantum groups corresponds to a ...
Sergey Neshveyev, M. Yamashita
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Tensor Network Renormalization with Fusion Charges—Applications to 3D Lattice Gauge Theory
Universe, 2020 Tensor network methods are powerful and efficient tools for studying the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions.
William J. Cunningham +2 more
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