Algebras

• Catalog of Algebras
• Quantum Groups

Free associative algebras and quotients

• 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

Finite dimensional algebras

• Finite-Dimensional Algebras
• Elements of Finite Algebras
• Ideals of Finite Algebras
• Morphisms Between Finite Algebras

Named associative algebras

• Affine nilTemperley Lieb Algebra of type A
• Askey-Wilson Algebras
• Diagram and Partition Algebras
• Clifford Algebras
• Cluster algebras
• Descent Algebras
• 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

Hecke algebras

• Ariki-Koike Algebras
• Iwahori-Hecke Algebras
• Nil-Coxeter Algebra
• Yokonuma-Hecke Algebras

Various associative algebras

• Associated Graded Algebras To Filtered Algebras
• Cellular Basis
• Commutative Differential Graded Algebras
• Q-Systems
• Splitting Algebras

Non-associative 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
  • The main classes to work with Lie conformal algebras
  • Implemented examples of Lie Conformal Algebras
  • See also
• Jordan Algebras
• Free Dendriform Algebras
• Free Pre-Lie Algebras
• Shuffle algebras
• Free Zinbiel Algebras

Indices and Tables

• Index

• Module Index

• Search Page