Operator representations of \(\mathcal{U}_ q(sl_ 2(\mathbb{R}))\)
From MaRDI portal
Publication:1915211
DOI10.1007/BF00416024zbMath0862.17012OpenAlexW24569106MaRDI QIDQ1915211
Publication date: 16 July 1996
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00416024
self-adjoint operatorquantum planeoperator representationsquantized universal enveloping algebranon-self-adjoint operatorscompact quantum groupintegrable representationsHopf \(*\)-algebranon-compact quantum group
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representations of topological algebras with involution (46K10) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)
Related Items
Self-dual continuous series of representations for \(\mathcal U_q(sl(2))\) and \(\mathcal U_q(osp(1|2))\), Positive representations with zero Casimirs, On the continuous series for \(\widehat{sl(2,\mathbb R)}\), Commutativity up to a factor: more results and the unbounded case, UNITARY REPRESENTATIONS OF NONCOMPACT QUANTUM GROUPS AT ROOTS OF UNITY, Discrete series of representations for the modular double of the quantum group \(U_q (sl(2, \mathbb R))\), A family of new Borel subalgebras of quantum groups, RECENT PROGRESS IN LIOUVILLE FIELD THEORY (REVIEW), A class of Hilbert space representations of the quantum plane and the quantum algebra \(U_q(\text{sl}_2)\), Representations of the \(q\)-deformed Lie algebra of the group of motions of the Euclidean plane
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
- Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
- \(q\)-deformed orthogonal and pseudo-orthogonal algebras and their representations
- Integrable operator representations of \(\mathbb{R}_ q^ 2\), \(X_{q,\gamma}\) and \(SL_ q(2,\mathbb{R})\)
- Quantum group \(\text{SU}(1,1)\rtimes\mathbb Z_ 2\) and ``super-tensor products
- Unbounded operator algebras and representation theory.
- An Operator-Theoretic Approach to a Cocycle Problem in the Complex Plane
