Orlik-Solomon algebra

Definition 9.29. The quotient algebra OS M) = E M)/Ios is called the Orlik-Solomon algebra of the matroid M. 

Definition 9.30. Assume that we are given an arbitrary A and B open in AU B, a matroid M, and a weight function w, associating a real number to each closed set in M of rank 1. Its Orlik-Solomon algebra OS M) can be made into a cochain complex OS M), called the Orlik-Solomon cochain... 

The Orlik-Solomon algebra and Orlik-Solomon cochain complex are cornerstones of a whole direction within arrangement theory. We recommend starting with Orlik Solomon, [OS80], and Yuzvinsky, [YuzOl], and proceeding with the references in the second paper. 

YuzOl] S. Yuzvinsky, Orlik-Solomon algebras in algebra and topology (Russian), Uspekhi Mat. Nauk 56 (2001), no. 2(338), 87-166 translation in Russian Math. Surveys 56 (2001), no. 2, 293-364. 

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