q-Onsager algebra
E654981
The q-Onsager algebra is a quantum deformation of the Onsager algebra that plays a key role in the study of integrable systems and quantum groups.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
associative algebra
ⓘ
deformation of Onsager algebra ⓘ infinite-dimensional algebra ⓘ quantum algebra ⓘ |
| admits |
finite-dimensional representations
ⓘ
infinite-dimensional representations ⓘ |
| generalizes | Dolan–Grady relations NERFINISHED ⓘ |
| hasApplicationsIn |
Bethe ansatz–type methods
ⓘ
exact solvable models ⓘ spectral analysis of transfer matrices ⓘ |
| hasCentralElement | Casimir-type elements (in certain realizations) ⓘ |
| hasConnectionTo |
Askey–Wilson polynomials
NERFINISHED
ⓘ
orthogonal polynomials ⓘ q-orthogonal polynomials ⓘ |
| hasDefiningGenerators | two generators A0 and A1 ⓘ |
| hasDefiningRelations | q-deformed Dolan–Grady relations ⓘ |
| hasParameter | q ⓘ |
| hasProperty |
non-cocommutative in its quantum group realizations
ⓘ
q-dependence in commutation relations ⓘ |
| hasRepresentationTheoryRelatedTo |
U_q(sl_2)
NERFINISHED
ⓘ
coideal subalgebras of quantum groups ⓘ |
| hasResearchTopic |
classification of its representations
ⓘ
connections with reflection equation algebras ⓘ construction of its PBW bases ⓘ realizations in terms of q-oscillators ⓘ |
| hasStructure | Poincaré–Birkhoff–Witt-type basis (PBW-type) NERFINISHED ⓘ |
| hasSymmetryRoleIn | boundary conditions of integrable models ⓘ |
| isConnectedTo |
K-matrices in integrable models
ⓘ
reflection equation ⓘ |
| isDefinedOver | a field containing complex numbers ⓘ |
| isObjectOfStudyInWorksBy |
Baseilhac
NERFINISHED
ⓘ
Koizumi NERFINISHED ⓘ Terwilliger NERFINISHED ⓘ |
| isQuantumDeformationOf | Onsager algebra NERFINISHED ⓘ |
| isRelatedTo |
Askey–Wilson algebra
NERFINISHED
ⓘ
integrable systems ⓘ quantum groups ⓘ quantum integrable models ⓘ tridiagonal pairs ⓘ |
| isStudiedIn |
algebraic combinatorics
ⓘ
mathematical physics ⓘ representation theory ⓘ |
| isSubstructureOf | certain coideal subalgebras of U_q(sl_2) ⓘ |
| isUsedIn |
XXZ spin chain with boundary
ⓘ
boundary integrable models ⓘ quantum spin chains ⓘ |
| reducesTo | Onsager algebra when q → 1 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.