On Hochschild cohomology of orders. (Q1423843)

For a class of tiled orders \(\Lambda\) close to hereditary orders, the authors calculate the Hochschild cohomology ring \(\text{HH}(\Lambda)\), generalizing previous work by \textit{K. Sanada} [J. Algebra 176, No. 3, 786-805 (1995; Zbl 0837.16010)]. They show first that \(\Lambda\) admits a two-sided projective resolution \[ \Lambda\rightarrowtail P_1\to P_0\twoheadrightarrow\Lambda. \] This gives \(\text{HH}(\Lambda)\cong R[x]/(ax)\), where \(a\) is an invariant of \(\Lambda\), and \(x\) is a cocycle of degree 2.