Cohomology for operator algebras: The Mayer-Vietoris sequence
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For an inclusion BA of operator algebras we introduce the B-nil cohomology groupsHn(A|B), which can be easier to compute than the standard cohomology groupsHn(A). We then develop two long exact sequences, the first linkingHn(A|B),Hn(A) andHn(B), the second corresponding to the Mayer-Vietoris sequence of algebraic topology. These sequences provide powerful computational tools, as illustrated by the examples in the last two sections of the paper. 1997 Academic Press.