Canonical basis.html



In mathematics, the notion of canonical basis refers to a basis of an algebraic structure which is canonical in a sense that depends on the precise context:

• In a coordinate space, and more generally in a free module, it refers to the standard basis defined by the Kronecker delta.
• In a polynomial ring, it refers to its standard basis given by the monomials, (Xⁱ)_i.
• For finite extension fields, it means the polynomial basis.
• In representation theory, Lusztig's canonical basis and closely related Kashiwara's crystal basis in quantum groups and their representations (cf. Littelmann path model).

See also

• Canonical
• Canonical form
• Normal form
• Polynomial basis
• Normal basis
• Change of bases

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