Koszul complex (Q2107)

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

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2778246876

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Koszul complex

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/m/02kz0y

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{\begin{aligned}&s\in E^{\vee }\\&0\to \bigwedge ^{\dim _{R}E}E{\overset {d}{\to }}\bigwedge ^{\dim _{R}E-1}E\to \dotsb \to \bigwedge ^{1}E{\overset {d}{\to }}R\to 0\\&d_{k}(e_{1}\wedge \dotsb \wedge e_{k})=\sum _{i=1}^{k}(-1)^{i+1}s(e_{i})e_{1}\wedge \dotsb \wedge {\hat {e}}_{i}\wedge \dotsb \wedge e_{k}\end{aligned}}

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R

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E

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E^{\vee }

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Koszul_complex

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Koszul2.png
1,611 × 778; 56 KB

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Q6433699

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