Representations of the \(q\)-deformed Lie algebra of the group of motions of the Euclidean plane

DOI10.1006/JFAN.1998.3329zbMath0923.17018OpenAlexW2066679736MaRDI QIDQ1276405

Sergei D. Silvestrov, Lyudmyla Turowska

Publication date: 3 June 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1998.3329

zbMATH Keywords

representationsHilbert space operatorsgroup of motions\(q\)-deformed Lie-algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Linear symmetric and selfadjoint operators (unbounded) (47B25) Commutators, derivations, elementary operators, etc. (47B47)

Cites Work

• Analytic vectors
• Representations of relations connecting a collection of commuting selfadjoint operators with a nonselfadjoint one
• Representations of operator relations by means of unbounded operators and multidimensional dynamical systems
• Bäcklund transformations and new solutions of nonlinear wave equations in four-dimensional space-time
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• Unbounded operators satisfying non-Lie commutation relations
• Quantum \(E(2)\) group and its Pontryagin dual
• Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)
• Operator representations of \(\mathbb{R}_ q^ 2\)
• Duality for the quantum \(E(2)\) group
• Operator representations of \(\mathcal{U}_ q(sl_ 2(\mathbb{R}))\)
• \(q\)-deformed Euclidean algebras and their representations
• Induced representation of locally compact groups. I
• Vecteurs analytiques dans les représentations des groupes de Lie
• Deformation quantization for actions of 𝑅^{𝑑}
• Hilbert space representations of the graded analogue of the Lie algebra of the group of plane motions
• Wild problems in the theory of representations of *-algebras generated by generatrices and relations
• Infinite-dimensional group representations
• Locally compact transformation groups and 𝐶*- algebras
• Simple facts about analytic vectors and integrability
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