 Koszul complex on central ring elements

ID: koszul-complex-on-central-ring-elements

For a possibly noncommutative ring and central

t_{i}

, the formal exterior basis gives free bimodules with differential

d (e_{i_{1}} \land \dots \land e_{i_{k}}) = \sum_{a} (- 1)^{a - 1} t_{i_{a}} e_{i_{1}} \land \dots e_{i_{a}} \dots \land e_{i_{k}}

. Centrality makes this a bimodule differential. Pairwise cancellation proves

d^{2} = 0

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