Eu, Ching-Hwa The product in the Hochschild cohomology ring of preprojective algebras of Dynkin quivers. (English) Zbl 1189.16009 J. Algebra 320, No. 4, 1477-1530 (2008). Summary: We compute the cup product structure of the preprojective algebras of Dynkin quivers of type \(D\) and \(E\) over a field of characteristic zero. This is a continuation of the work done by P. Etingof, C.-H. Eu [Mosc. Math. J. 7, No. 4, 601-612 (2007; Zbl 1138.16004)] where the additive structure of the Hochschild cohomology (together with its grading) was computed. Together with the results of K. Erdmann, N. Snashall [J. Algebra 205, No. 2, 391-412 (1998; Zbl 0937.16012), ibid. 205, No. 2, 413-434 (1998; Zbl 0937.16013)] (where the \(A\)-case was studied), this yields a complete description of the product in the Hochschild cohomology of \(ADE\) quivers over a field of characteristic zero. Cited in 10 Documents MSC: 16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) 16G20 Representations of quivers and partially ordered sets Keywords:preprojective algebras; Dynkin quivers; Hochschild cohomology; cup products; Hochschild homology Citations:Zbl 1138.16004; Zbl 0937.16012; Zbl 0937.16013 PDFBibTeX XMLCite \textit{C.-H. Eu}, J. Algebra 320, No. 4, 1477--1530 (2008; Zbl 1189.16009) Full Text: DOI arXiv References: [1] Crawley-Boevey, W.; Etingof, P.; Ginzburg, V., Noncommutative geometry and quiver algebras · Zbl 1111.53066 [2] Etingof, P.; Eu, C., Hochschild and cyclic homology of preprojective algebras of ADE quivers · Zbl 1138.16004 [3] Erdmann, K.; Snashall, N., On Hochschild cohomology of preprojective algebras. I, J. Algebra. J. Algebra, J. Algebra, 205, 2, 413-434 (1998), II · Zbl 0937.16013 [4] Eu, C., The calculus structure of the Hochschild homology/cohomology of preprojective algebras of Dynkin quivers · Zbl 1189.16010 [5] Malkin, A.; Ostrik, V.; Vybornov, M., Quiver varieties and Lusztig’s algebra · Zbl 1120.16015 [6] A. Schofield, Wild algebras with periodic Auslander-Reiten translate, preprint; A. Schofield, Wild algebras with periodic Auslander-Reiten translate, preprint This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.