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Implement down-up algebras and their Verma modules #35484

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May 22, 2023
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Implement down-up algebras and their Verma modules #35484

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c130aef
Initial implementation of down-up algebras and their Verma modules.
tscrim Apr 12, 2023
2deed7a
Update down_up_algebra.py
fchapoton Apr 16, 2023
5998596
Update down_up_algebra.py
fchapoton Apr 16, 2023
49097fe
Changing degree into weight for Verma module elements.
tscrim Apr 18, 2023
3ccebf0
Adding some more examples and doc.
tscrim Apr 18, 2023
8b57537
Fixing a few typos.
tscrim Apr 18, 2023
c962e4f
Improving the documentation.
tscrim May 8, 2023
a932b10
Fixing some details and a few slight doc tweaks.
tscrim May 9, 2023
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1 change: 1 addition & 0 deletions src/doc/en/reference/algebras/index.rst
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Expand Up @@ -48,6 +48,7 @@ Named associative algebras
sage/algebras/clifford_algebra
sage/algebras/cluster_algebra
sage/combinat/descent_algebra
sage/algebras/down_up_algebra
fusion_rings
sage/algebras/hall_algebra
sage/combinat/posets/incidence_algebras
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8 changes: 8 additions & 0 deletions src/doc/en/reference/references/index.rst
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Expand Up @@ -1123,6 +1123,10 @@ REFERENCES:
Achtzelle (Oktatope)", Verhand. Konik. Akad. Wetenschap,
Erste Sectie, 10 (1910)

.. [BR1998] Georgia Benkart and Tom Roby. *Down-up algebras*.
J. Algebra, **209** no. 1 (1999), pp. 305-335.
:doi:`10.1006/jabr.1998.7511`.

.. [Br2000] Kenneth S. Brown, *Semigroups, rings, and Markov chains*,
:arxiv:`math/0006145v1`.

Expand Down Expand Up @@ -1615,6 +1619,10 @@ REFERENCES:
\J. Algebr. Comb. **39** (2014) pp. 17-51.
:doi:`10.1007/s10801-013-0437-x`, :arxiv:`1108.1776`.

.. [CM2000] Paula A.A.B. Carvalho and Ian M. Musson. *Down-up algebras and
their representation theory*. J. Algebra. **228** no. 1, (2000),
pp. 286-310. :doi:`10.1006/jabr.1999.8263`

.. [CM2012] \M. Cabanes, I. Marin, *On ternary quotients of cubic Hecke
algebras*, Comm. Math. Phys. (2012), Volume 314, Issue 1,
pp 57-92. :doi:`10.1007/s00220-012-1519-7`, :arxiv:`1010.1465`.
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2 changes: 2 additions & 0 deletions src/sage/algebras/catalog.py
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Expand Up @@ -23,6 +23,7 @@
- :class:`algebras.Descent <sage.combinat.descent_algebra.DescentAlgebra>`
- :class:`algebras.DifferentialWeyl
<sage.algebras.weyl_algebra.DifferentialWeylAlgebra>`
- :class:`algebras.DownUp <sage.algebras.down_up_algebra.DownUpAlgebra>`
- :class:`algebras.Exterior <sage.algebras.clifford_algebra.ExteriorAlgebra>`
- :class:`algebras.FiniteDimensional
<sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra.FiniteDimensionalAlgebra>`
Expand Down Expand Up @@ -134,6 +135,7 @@
lazy_import('sage.algebras.quantum_groups.quantum_group_gap', 'QuantumGroup')
lazy_import('sage.algebras.quantum_groups.ace_quantum_onsager',
'ACEQuantumOnsagerAlgebra', 'AlternatingCentralExtensionQuantumOnsager')
lazy_import('sage.algebras.down_up_algebra', 'DownUpAlgebra', 'DownUp')
lazy_import('sage.algebras.yangian', 'Yangian')

del lazy_import # We remove the object from here so it doesn't appear under tab completion
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