Reality in the differential calculus on \(q\)-Euclidean spaces

DOI10.1007/BF00398308zbMath0765.17019arXivhep-th/9205003MaRDI QIDQ1196091

O. V. Ogievetskij, Bruno Zumino

Publication date: 29 November 1992

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

Full work available at URL: https://arxiv.org/abs/hep-th/9205003

zbMATH Keywords

derivatives\(R\)-matrixdifferentialsnoncommutative differential calculusEuclidean quantum spacenonlinear reality structurereal Laplacian

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)

Related Items (18)

DRINFEL'D TWIST AND q-DEFORMING MAPS FOR LIE GROUP COVARIANT HEISENBERG ALGEBRAE ⋮ Group theoretical foundations of fractional supersymmetry ⋮ A q-deformation of the Coulomb problem ⋮ Integration on quantum Euclidean space and sphere ⋮ Realization of \(U_ q(so(N))\) within the differential algebra on \(\mathbb{R}_ q^ N\) ⋮ Quasi-\(*\) structure on \(q\)-Poincaré algebras ⋮ Generalized q-exponentials related to orthogonal quantum groups and Fourier transformations of noncommutative spaces ⋮ On the deformability of Heisenberg algebras ⋮ \(\mathrm{GL}_{r,s}(n)\)-covariant differential calculi on the quantum \(n\)-space ⋮ The Euclidean Hopf algebra U q(e N) and its fundamental Hilbert-space representations ⋮ *-structures on braided spaces ⋮ ON THE HERMITICITY OF q-DIFFERENTIAL OPERATORS AND FORMS ON THE QUANTUM EUCLIDEAN SPACES $\mathbb{R}_q^N$ ⋮ q -quaternions and q-deformed su(2) instantons ⋮ The geometry of the quantum Euclidean space ⋮ Field theory on the \(q\)-deformed fuzzy sphere. I. ⋮ Free particle in \(q\)-deformed configuration space ⋮ Quantum Clifford algebras from spinor representations ⋮ ANALYSIS ON q-DEFORMED QUANTUM SPACES

Cites Work

• Bicovariant differential calculus on quantum groups \(SU_ q(N)\) and \(SO_ q(N)\)
• Differential operators on quantum spaces for \(GL_ q(n)\) and \(SO_ q(n)\)

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