Algebraic q-integration and Fourier theory on quantum and braided spaces

DOI10.1063/1.530644zbMath0826.17018arXivhep-th/9402037OpenAlexW1982015938MaRDI QIDQ4837164

Achim Kempf, Shahn Majid

Publication date: 4 July 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9402037

zbMATH Keywords

Jackson \(q\)-integralbraid statisticsbraided group of functionsintegration on quantum planes

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative topology (46L85) Noncommutative differential geometry (46L87) Braid groups; Artin groups (20F36)

Related Items (29)

Hodge star as braided Fourier transform ⋮ Maximal localization in the presence of minimal uncertainties in positions and in momenta ⋮ Integration on quantum Euclidean space and sphere ⋮ Diffusion on braided spaces ⋮ Conservation laws for linear equations on braided linear spaces ⋮ Braided Line and Counting Fixed Points ofGL(d, 𝔽_q) ⋮ Quasi-\(*\) structure on \(q\)-Poincaré algebras ⋮ Lagrangian formalism over graded algebras ⋮ Braided oscillators ⋮ Conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces ⋮ Generalized q-exponentials related to orthogonal quantum groups and Fourier transformations of noncommutative spaces ⋮ q-epsilon tensor for quantum and braided spaces ⋮ Basic Fourier transform on the space of entire functions of logarithm order 2 ⋮ Operator identities in \(q\)-deformed Clifford analysis ⋮ On quantum field theory with nonzero minimal uncertainties in positions and momenta ⋮ *-structures on braided spaces ⋮ ON THE HERMITICITY OF q-DIFFERENTIAL OPERATORS AND FORMS ON THE QUANTUM EUCLIDEAN SPACES $\mathbb{R}_q^N$ ⋮ SOME ALGEBRAICAL, COMBINATORIAL AND ANALYTICAL PROPERTIES OF PARAGRASSMANN VARIABLES ⋮ Plancherel identity for semisimple hopf algebras ⋮ Quantum groups and noncommutative geometry ⋮ The Urbanik generalized convolutions in the non-commutative probability and a forgotten method of constructing generalized convolution ⋮ The quantum geometry of spin and statistics ⋮ \(q\)-exponentials on quantum spaces ⋮ ON A CONVOLUTION FOR q-NORMAL ELEMENTS ⋮ A braided interpretation of fractional supersymmetry in higher dimensions ⋮ Braided bosonization and inhomogeneous quantum groups ⋮ q-Oscillator Algebra And d-Orthogonal Polynomials ⋮ ANALYSIS ON q-DEFORMED QUANTUM SPACES ⋮ On the braided Fourier transform on the n-dimensional quantum space

Cites Work

• Quantum group-symmetric Fock spaces with Bargmann-Fock representation
• \(q\)-deformed Poincaré algebra
• Quantum and braided-Lie algebras
• Braided groups and quantum Fourier transform
• Free particle in \(q\)-deformed configuration space
• THE SO_q(N, R)-SYMMETRIC HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE ${\bf R}_q^N$ AND ITS HILBERT SPACE STRUCTURE
• A QUANTUM LORENTZ GROUP
• Examples of braided groups and braided matrices
• C-statistical quantum groups and Weyl algebras
• Braided momentum in the q-Poincaré group
• Quantum group symmetric Bargmann–Fock space: Integral kernels, Green functions, driving forces
• Quantum and braided linear algebra
• Free braided differential calculus, braided binomial theorem, and the braided exponential map
• On the addition of quantum matrices
• q-Euclidean space and quantum Wick rotation by twisting

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