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mathematics (516) 516
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2016, Graduate studies in mathematics, ISBN 9781470423070, Volume 174, xii, 295 pages
Book
2012, Mathematical surveys and monographs, ISBN 9780821875810, Volume 181, xvii, 367
Book
Communications in Algebra, ISSN 0092-7872, 09/2019, Volume 47, Issue 9, pp. 3597 - 3613
For a gentle algebra , we obtain an explicit description of the quiver with relations for the Cohen-Macaulay Auslander algebra... 
Cohen-Macaulay Auslander algebra | gentle algebra | Gorenstein projective module | CM-finiteness | Cohen–Macaulay Auslander algebra | MATHEMATICS | CATEGORIES | Modules | Algebra | Representations
Journal Article
Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 859 - 887
We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of Ext-finite hereditary abelian categories... 
Shod algebras | Derived categories | Silting theory | Torsion pairs | MATHEMATICS | TILTED ALGEBRAS | MUTATION | AUSLANDER-REITEN COMPONENTS | OBJECTS | SMALL HOMOLOGICAL DIMENSIONS | Silt | Algebra
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2018, Volume 326, pp. 200 - 240
We generalize the notions of n-cluster tilting subcategories and τ-selfinjective algebras into n-precluster tilting subcategories and τ... 
Cluster tilting | Relative homological algebra | Auslander–Reiten theory | Auslander algebra | SUBCATEGORIES | SEQUENCES | DOMINANT DIMENSION | MATHEMATICS | SYZYGY MODULES | REPRESENTATION-THEORY | RELATIVE HOMOLOGY | EXACT CATEGORIES | Auslander-Reiten theory | DUALITY | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2019, Volume 351, pp. 1139 - 1200
We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander–Reiten theory... 
Homological embedding | Auslander–Reiten quiver | Auslander–Reiten theory | Cluster-tilting | Nakayama algebras | MATHEMATICS | Auslander-Reiten theory | Auslander-Reiten quiver | QUIVERS | CATEGORIES | EQUIVALENCE | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 02/2014, Volume 252, pp. 292 - 342
From the viewpoint of higher dimensional Auslander–Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite... 
Preprojective algebra | Fano algebra | Auslander–Reiten theory | n-representation finite algebra | Representation dimension | Auslander-Reiten theory | N-representation finite algebra | MATHEMATICS | FINITE ALGEBRAS | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2011, Volume 226, Issue 2, pp. 1973 - 2019
Journal Article
Journal of Algebra, ISSN 0021-8693, 08/2018, Volume 508, pp. 475 - 511
We provide a combinatorial algorithm for constructing the stable Auslander–Reiten component containing a given indecomposable module of a symmetric special biserial algebra using only information from its underlying Brauer graph... 
Brauer graph algebras | Finite dimensional algebras | Representation theory | Special biserial algebras | Auslander–Reiten theory | String modules | String combinatorics | MATHEMATICS | Auslander-Reiten theory
Journal Article
Journal of Algebra, ISSN 0021-8693, 10/2019, Volume 536, pp. 149 - 169
We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs... 
Auslander's Theorem | Filtered group actions | Fixed rings | Generalized Weyl algebras | MATHEMATICS | DEFORMATIONS | AUTOMORPHISMS | Mathematics - Rings and Algebras
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 11/2017, Volume 16, Issue 11
We introduce and study the class of right ADA algebras. An artin algebra is right ADA if every indecomposable projective module lies in the left or in the right part of its module category... 
Right ADA algebras | Auslander-Reiten components | right sections | MATHEMATICS | MATHEMATICS, APPLIED | SUBCATEGORIES | REPRESENTATION-THEORY | SKEW GROUP-ALGEBRAS
Journal Article
Journal of Algebra, ISSN 0021-8693, 07/2019, Volume 530, pp. 146 - 162
We determine the structure of all finite-dimensional selfinjective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice. 
Auslander-Reiten quiver | Selfinjective algebra | Orbit algebra | Stable slice | Tilted algebra | Computer science | Algebra
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2011, Volume 226, Issue 1, pp. 1 - 61
The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander... 
Cluster tilting | Higher almost split sequence | Higher Auslander algebra | GORENSTEIN | TRIANGULATED CATEGORIES | MATHEMATICS | MODULES | ORTHOGONAL SUBCATEGORIES | SPLIT-SEQUENCES | DIMENSION | REITEN QUIVERS | MUTATION | PREPROJECTIVE ALGEBRAS | CALABI-YAU | Business presentations
Journal Article
Journal Article
Algebras and representation theory, ISSN 1572-9079, 2019, Volume 23, Issue 3, pp. 1197 - 1235
We study a finite-dimensional algebra Lambda from a Postnikov diagram D in a disk, obtained from the dimer algebra of Baur-King-Marsh by factoring out the ideal generated by the boundary idempotent... 
Dimer model | MATHEMATICS | Higher dimensional Auslander-Reiten theory | QUIVERS | Preprojective algebra | Grassmannian cluster algebra | Postnikov diagram | Jacobian algebra | CLUSTER | CATEGORIES | Self-injective algebra
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2011, Volume 363, Issue 12, pp. 6575 - 6614
We introduce the notion of n-representation-finiteness, generalizing representation-finite hereditary algebras... 
Morphisms | Admissible sets | Algebra | Mathematical theorems | Mathematical objects | Functors | Quivers | Arrows | Vertices | MATHEMATICS | MODULES | ORTHOGONAL SUBCATEGORIES | QUIVERS | AUSLANDER ALGEBRAS | CLUSTER | CATEGORIES
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2018, Volume 51, Issue 4, p. 45201
Journal Article
Journal of Algebra and its Applications, ISSN 0219-4988, 02/2018, Volume 17, Issue 2
We classify Borel-Schur algebras having finite representation type. We also determine Auslander-Reiten sequences for a large class of simple modules over Borel-Schur algebras... 
Schur algebra | Borel-Schur algebra | Auslander-Reiten sequences | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTATION-THEORY | MODULES | PROJECTIVE-RESOLUTIONS | SPLIT-SEQUENCES | WEYL | Mathematics - Representation Theory
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2017, Volume 285, Issue 1, pp. 367 - 395
We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective–injective... 
Primary 16G60 | Representation variety | 14M15 | Auslander algebra | Mathematics, general | Quiver Grassmannian | Tilting theory | Mathematics | Secondary 14L30 | MATHEMATICS | VARIETIES | Algebra
Journal Article
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