Koszul complex (Q2107)

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construction of homological algebra used in commutative agebra

Language	Label	Description	Also known as
English	Koszul complex	construction of homological algebra used in commutative agebra

Statements

differential graded-commutative algebra

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Jean-Louis Koszul

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defining formula

\begin{matrix} s \in E^{\lor} \\ 0 \to ⋀^{\dim_{R} E} E \overset{d}{\to} ⋀^{\dim_{R} E - 1} E \to \dots \to ⋀^{1} E \overset{d}{\to} R \to 0 \\ d_{k} (e_{1} \land \dots \land e_{k}) = \sum_{i = 1}^{k} (- 1)^{i + 1} s (e_{i}) e_{1} \land \dots \land {\hat{e}}_{i} \land \dots \land e_{k} \end{matrix}

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in defining formula

R

symbol represents

commutative ring

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E

symbol represents

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E^{\lor}

symbol represents

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mathematical concept

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Koszul2.png
1,611 × 778; 56 KB

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Identifiers

Microsoft Academic ID

2778246876

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Koszul complex

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/m/02kz0y

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Encyclopedia of Mathematics article ID

Koszul_complex

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Sitelinks

mathematics(0 entries)

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