gh-36907: Implementation of the quantum oscillator algebra

    
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We provide an implementation of the quantum oscillator algebra as
defined in a recent book of Kuniba. This has been used to construct
representations of the quantum coordinate rings for simple Lie algebras
and solutions to the Yang-Baxter, reflection, and tetrahedron equations.
We also implement its Fock space representation.

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URL: #36907
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton

src/doc/en/reference/algebras/index.rst

@@ -61,6 +61,7 @@ Named associative algebras
  sage/algebras/quantum_clifford
  sage/algebras/quantum_groups/quantum_group_gap
  sage/algebras/quantum_matrix_coordinate_algebra
+ sage/algebras/quantum_oscillator
  sage/algebras/quatalg/quaternion_algebra
  sage/algebras/rational_cherednik_algebra
  sage/algebras/schur_algebra

src/doc/en/reference/references/index.rst

@@ -4060,6 +4060,11 @@ REFERENCES:
  study of the subgroups of the modular group", American
  Journal of Mathematics 113 (1991), no 6, 1053-1133
 
+.. [Kuniba2022] Atsuo Kuniba,
+ *Quantum Groups in Three-Dimensional Integrability*.
+ Theoretical and Mathematical Physics, Springer. 2022.
+ :doi:`10.1007/978-981-19-3262-5`.
+
 .. [Kur2008] Chris Kurth, "K Farey package for Sage",
  http://wayback.archive-it.org/855/20100510123900/http://www.public.iastate.edu/~kurthc/research/index.html
 

src/sage/algebras/catalog.py

@@ -59,6 +59,8 @@
  <sage.algebras.quantum_matrix_coordinate_algebra.QuantumGL>`
 - :class:`algebras.QuantumMatrixCoordinate
  <sage.algebras.quantum_matrix_coordinate_algebra.QuantumMatrixCoordinateAlgebra>`
+- :class:`algebras.QuantumOscillator
+ <sage.algebras.quantum_oscillator.QuantumOscillatorAlgebra>`
 - :class:`algebras.QSym <sage.combinat.ncsf_qsym.qsym.QuasiSymmetricFunctions>`
 - :class:`algebras.Partition <sage.combinat.diagram_algebras.PartitionAlgebra>`
 - :class:`algebras.PlanarPartition <sage.combinat.diagram_algebras.PlanarAlgebra>`
@@ -128,6 +130,7 @@
 lazy_import('sage.combinat.ncsf_qsym.qsym', 'QuasiSymmetricFunctions', 'QSym')
 lazy_import('sage.combinat.grossman_larson_algebras', 'GrossmanLarsonAlgebra', 'GrossmanLarson')
 lazy_import('sage.algebras.quantum_clifford', 'QuantumCliffordAlgebra', 'QuantumClifford')
+lazy_import('sage.algebras.quantum_oscillator', 'QuantumOscillatorAlgebra', 'QuantumOscillator')
 lazy_import('sage.algebras.quantum_matrix_coordinate_algebra',
  'QuantumMatrixCoordinateAlgebra', 'QuantumMatrixCoordinate')
 lazy_import('sage.algebras.quantum_matrix_coordinate_algebra', 'QuantumGL')