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Algebras
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Sage 9.8 Reference Manual
  • Home - Algebras
  • Catalog of Algebras
  • Quantum Groups
    • Alternating Central Extension Quantum Onsager Algebra
    • Fock Space
    • \(q\)-Numbers
    • Quantum Group Representations
  • Free algebras
  • Free algebra elements
  • Free associative unital algebras, implemented via Singular’s letterplace rings
  • Weighted homogeneous elements of free algebras, in letterplace implementation
  • Homogeneous ideals of free algebras
  • Finite dimensional free algebra quotients
  • Free algebra quotient elements
  • Tensor Algebras
  • Finite-Dimensional Algebras
  • Elements of Finite Algebras
  • Ideals of Finite Algebras
  • Morphisms Between Finite Algebras
  • Affine nilTemperley Lieb Algebra of type A
  • Askey-Wilson Algebras
  • Diagram and Partition Algebras
  • Clifford Algebras
  • Cluster algebras
  • Descent Algebras
  • Fusion Rings
    • Fusion Rings
    • The F-Matrix of a Fusion Ring
    • Fast F-Matrix Methods
    • Fast Fusion Ring Methods for Computing Braid Group Representations
    • Arithmetic Engine for Polynomials as Tuples
    • Shared Memory Managers for F-Symbol Attributes
  • Hall Algebras
  • Incidence Algebras
  • Group algebras
  • Grossman-Larson Hopf Algebras
  • Möbius Algebras
  • Orlik-Terao Algebras
  • Orlik-Solomon Algebras
  • Partition/Diagram Algebras
  • Quantum Clifford Algebras
  • Quantum Groups Using GAP’s QuaGroup Package
  • Quantum Matrix Coordinate Algebras
  • Quaternion Algebras
  • Rational Cherednik Algebras
  • Schur algebras for \(GL_n\)
  • The Steenrod algebra
  • Steenrod algebra bases
  • Miscellaneous functions for the Steenrod algebra and its elements
  • Multiplication for elements of the Steenrod algebra
  • Weyl Algebras
  • Yangians
  • Ariki-Koike Algebras
  • Iwahori-Hecke Algebras
  • Nil-Coxeter Algebra
  • Yokonuma-Hecke Algebras
  • Cubic Hecke Algebras
    • Cubic Hecke Algebras
    • Cubic Hecke Base Rings
    • Cubic Hecke matrix representations
  • Finite dimensional graded commutative algebras
  • Commutative Differential Graded Algebras
  • Associated Graded Algebras To Filtered Algebras
  • Cellular Basis
  • Q-Systems
  • \(q\)-Commuting Polynomials
  • Splitting Algebras
  • Lie Algebras
    • Abelian Lie Algebras
    • Affine Lie Algebras
    • The Baker-Campbell-Hausdorff formula
    • Classical Lie Algebras
    • Examples of Lie Algebras
    • Free Lie Algebras
    • Heisenberg Algebras
    • Lie Algebras
    • Lie Algebra Elements
    • Homomorphisms of Lie Algebras
    • Nilpotent Lie algebras
    • Onsager Algebra
    • The Poincare-Birkhoff-Witt Basis For A Universal Enveloping Algebra
    • Quotients of Lie algebras
    • Rank Two Heisenberg-Virasoro Algebras
    • Lie Algebras Given By Structure Coefficients
    • Subalgebras and ideals of Lie algebras
    • Symplectic Derivation Lie Algebras
    • Verma Modules
    • Virasoro Algebra and Related Lie Algebras
  • Lie Conformal Algebras
    • Lie Conformal Algebra
    • Examples of Lie Conformal Algebras
    • Lie Conformal Algebra Element
    • Abelian Lie Conformal Algebra
    • Affine Lie Conformal Algebra
    • Bosonic Ghosts Lie Conformal Algebra
    • Fermionic Ghosts Super Lie Conformal Algebra
    • Free Bosons Lie Conformal Algebra
    • Free Fermions Super Lie Conformal Algebra.
    • N=2 Super Lie Conformal Algebra
    • Neveu-Schwarz Super Lie Conformal Algebra
    • Virasoro Lie Conformal Algebra
    • Weyl Lie Conformal Algebra
    • Finitely and Freely Generated Lie Conformal Algebras.
    • Freely Generated Lie Conformal Algebras
    • Graded Lie Conformal Algebras
    • Lie Conformal Algebras With Basis
    • Lie Conformal Algebras With Structure Coefficients
  • Jordan Algebras
  • Free Dendriform Algebras
  • Free Pre-Lie Algebras
  • Shuffle algebras
  • Free Zinbiel Algebras
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Quantum Groups#

  • Alternating Central Extension Quantum Onsager Algebra
  • Fock Space
  • \(q\)-Numbers
  • Quantum Group Representations
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Alternating Central Extension Quantum Onsager Algebra
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Catalog of Algebras
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