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dc.contributor.authorPRESOTTO, Dennis-
dc.contributor.authorde Thanhoffer de Volcsey, Louis-
dc.identifier.citationJOURNAL OF ALGEBRA, 470, p. 450-483-
dc.description.abstractIn this note we consider a notion of relative Frobenius pairs of commutative rings S/R. To such a pair, we associate an N-graded R -algebra which has a simple description and coincides with the preprojective algebra of a quiver with a single central node and several outgoing edges in the split case. If the rank of S over R is 4 and R is Noetherian, we prove that the generalized preprojective algebra is itself Noetherian and finite over its center and that it is finitely generated projective in each degree. We also prove that generalized preprojective algebras are of finite global dimension if the rings R and S are regular.-
dc.description.sponsorshipDuring the creation of this paper, the first author was a Ph.D.student at the Univer-sity of Hasselt, Belgium. The second author was funded by a Ph.D.fellowship with the FWO Flanders.-
dc.rightsC) 2016 Elsevier Inc. All rights reserved.-
dc.subject.othernon-commutative algebras; preprojective algebras-
dc.titleSome generalizations of preprojective algebras and their properties-
dc.typeJournal Contribution-
dc.relation.references[1] M. Atiyah, I. Macdonald, Introduction to Commutative Algebra, Addison–Wesley Publishing Company, 1969. [2] H. Bass, Algebraic K-Theory, W.A. Benjamin, Inc., 1968. [3] R. Bocklandt, T. Schedler, M. Wemyss, Superpotentials and higher order derivations, J. Pure Appl. Algebra 214 (9) (2010) 1501–1522. [4] W. Crawley-Boevey, M.P. Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (3) (1998) 605–635. [5] P. Etingof, C. Eu, Koszulity and the Hilbert series of preprojective algebras, Math. Res. Lett. 14 (4) (2007) 589–596. [6] A. Grothendieck, Rêvetement étales et groupe fondamental (SGA 1), Lecture Notes in Mathematics, vol. 224, Springer, 1971. [7] A. Grothendieck, J. Dieudonné, Éléments de géometrie algebrique III: étude cohomologique des faiscaux coherents, premiere partie (EGA 3a), Lecture Notes in Mathematics, vol. 11, IHES, 1971. [8] T. Lam, Exercises in Modules and Rings, Problem Books in Mathematics, Springer, 2007. [9] B. Poonen, Isomorphism types of commutative algebras of finite rank over an algebraically closed field, in: Computational Arithmetic Geometry, in: Contemp. Math., vol. 463, Amer. Math. Soc., Providence, RI, 2008, pp. 111–120. [10] M. Reid, The Du Val singularities An, Dn, E6, E7, E8, surf/more/DuVal.pdf, August 2016. [11] I. Reiten, M. Van den Bergh, Two-Dimensional Tame and Maximal Orders of Finite Representation Type, Memoirs of the American Mathematical Society, vol. 80, 1989, no. 408. [12] T. Schedler, Hochschild homology of preprojective algebras over the integers, arXiv:0704.3278, April 2007. [13] J.-P. Serre, Faisceaux algebriques coherents, Ann. of Math. 61 (2) (1955) 197–278.-
item.fulltextWith Fulltext-
item.fullcitationPRESOTTO, Dennis & de Thanhoffer de Volcsey, Louis (2017) Some generalizations of preprojective algebras and their properties. In: JOURNAL OF ALGEBRA, 470, p. 450-483.-
item.accessRightsOpen Access-
item.contributorPRESOTTO, Dennis-
item.contributorde Thanhoffer de Volcsey, Louis-
item.validationecoom 2018-
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