Periodic projective resolutions and Hochschild cohomology for basic hereditary orders. (Q854890)

Let \(\Lambda\) be a basic hereditary order over a discrete valuation ring with finite residue class field and let \(\Lambda^e\) be its enveloping algebra. An explicit projective resolution of \(\Lambda\) as a \(\Lambda^e\)-module is constructed; this resolution turns out to be periodic of period two. As a consequence, the Hochschild cohomology ring of \(\Lambda\) is determined. This generalises earlier work of the second named author [J. Algebra 176, No. 3, 786-805 (1995; Zbl 0837.16010)].