Koszul algebra (original) (raw)
Koszulalgebra är inom matematiken en en -algebra över vilken har en linjär minimal graderad fri resolution, d.v.s., det finns en exakt följd: Koszulalgebror är uppkallade efter den franska matematikern .
| Property | Value |
|---|---|
| dbo:abstract | In abstract algebra, a Koszul algebra is a graded -algebra over which the ground field has a linear minimal graded free resolution, i.e., there exists an exact sequence: Here, is the graded algebra with grading shifted up by , i.e. . The exponents refer to the -fold direct sum. Choosing bases for the free modules in the resolution, the chain maps are given by matrices, and the definition requires the matrix entries to be zero or linear forms. An example of a Koszul algebra is a polynomial ring over a field, for which the Koszul complex is the minimal graded free resolution of the ground field. There are Koszul algebras whose ground fields have infinite minimal graded free resolutions, e.g, . The concept is named after the French mathematician Jean-Louis Koszul. (en) Koszulalgebra är inom matematiken en en -algebra över vilken har en linjär minimal graderad fri resolution, d.v.s., det finns en exakt följd: Koszulalgebror är uppkallade efter den franska matematikern . (sv) |
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| rdfs:comment | Koszulalgebra är inom matematiken en en -algebra över vilken har en linjär minimal graderad fri resolution, d.v.s., det finns en exakt följd: Koszulalgebror är uppkallade efter den franska matematikern . (sv) In abstract algebra, a Koszul algebra is a graded -algebra over which the ground field has a linear minimal graded free resolution, i.e., there exists an exact sequence: Here, is the graded algebra with grading shifted up by , i.e. . The exponents refer to the -fold direct sum. Choosing bases for the free modules in the resolution, the chain maps are given by matrices, and the definition requires the matrix entries to be zero or linear forms. The concept is named after the French mathematician Jean-Louis Koszul. (en) |
| rdfs:label | Koszul algebra (en) Koszulalgebra (sv) |
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