Canonical basis

Canonical basis

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, (X^i)_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).

ee also

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


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