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21
HIGHER PREPROJECTIVE ALGEBRAS AND STABLY CALABIYAU PROPERTIES
, 2013
"... Abstract. In this paper, we give sufficient properties for a finite dimensional graded algebra to be a higher preprojective algebra. These properties are of homological nature, they use Gorensteiness and bimodule isomorphisms in the stable category of CohenMacaulay modules. We prove that these prop ..."
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Abstract. In this paper, we give sufficient properties for a finite dimensional graded algebra to be a higher preprojective algebra. These properties are of homological nature, they use Gorensteiness and bimodule isomorphisms in the stable category of CohenMacaulay modules. We prove that these properties are also necessary for 3preprojective algebras using [Kel11] and for preprojective algebras of higher representation finite algebras using [Dug12].
τ2stable tilting complexes over weighted projective lines. arXiv:1402.6036
, 2014
"... Abstract. Let X be a weighted projective line and cohX the associated categoy of coherent sheaves. We classify the tilting complexes T in Db(cohX) such that τ2T ∼ = T, where τ is the AuslanderReiten translation in Db(cohX). As an application of this result, we classify the 2representationfinite ..."
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Abstract. Let X be a weighted projective line and cohX the associated categoy of coherent sheaves. We classify the tilting complexes T in Db(cohX) such that τ2T ∼ = T, where τ is the AuslanderReiten translation in Db(cohX). As an application of this result, we classify the 2representationfinite algebras which are derivedequivalent to a canonical algebra. This complements IyamaOppermann’s classification of the iterated tilted 2representationfinite algebras. By passing to 3preprojective algebras, we obtain a classification of the selfinjective clustertilted algebras of canonicaltype. This complements Ringel’s classification of the selfinjective clustertilted algebras. 1.
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, 2006
"... We introduce the notion of mutation on the set of ncluster tilting subcategories in a triangulated category with AuslanderReitenSerre duality. Using this idea, we are able to obtain the complete classifications of rigid CohenMacaulay modules over certain Veronese subrings. 1 ..."
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We introduce the notion of mutation on the set of ncluster tilting subcategories in a triangulated category with AuslanderReitenSerre duality. Using this idea, we are able to obtain the complete classifications of rigid CohenMacaulay modules over certain Veronese subrings. 1
nrepresentationfinite algebras and . . .
"... We introduce the notion of nrepresentationfiniteness, generalizing representationfinite hereditary algebras. We establish the procedure of nAPR tilting, and show that it preserves nrepresentationfiniteness. We give some combinatorial description of this procedure, and use this to completely ..."
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We introduce the notion of nrepresentationfiniteness, generalizing representationfinite hereditary algebras. We establish the procedure of nAPR tilting, and show that it preserves nrepresentationfiniteness. We give some combinatorial description of this procedure, and use this to completely describe a class of nrepresentationfinite algebras called “type A”.