Representation Dimension and Quasi-hereditary Algebras

By Changchang Xi. 2002

82 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82a14dff0711b98972a2b07a42f4c787169d1383

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Citations in the corpus

On the representation dimension of tilted and laura algebras (2006, methodology): “The interest in the representation dimension was recently revived by works of Xi [25, 26] and also because of its relationship with the finitistic and the Nakayama conjectures: it was shown by Igusa and Todorov in [18] that if the representation dimension of an algebra is at most 3, then its finitis”
On the finitistic dimension conjecture, III: Related to the pair eAe⊆A (2008, methodology): “For further information about advances on the finitistic dimension conjecture as well as its relationship with other homological conjectures in the representation theory of Artin algebras, we may refer to [7,29, 30 ,33,34] and the references therein.”
Radical embeddings and representation dimension (2002, background): “R T ] 2 3 O ct DEDICATED TO THE MEMORY OF SHEILA BRENNER”
Auslander–Reiten theory revisited (2008, methodology): “In this subsection we shall recall the construction of 2-CY Frobenius categories with 2-cluster tilting objects given in joint work with Buan, Reiten and Scott [89, 37].”
Derived equivalences and stable equivalences of Morita type, I (2008, background): “For instance, the global, finitistic, dominant and representation dimensions all are invariants (see [8], [21], [50]).”
Finitistic dimension and Igusa-Todorov algebras (2009, background): “This was proved for (a) and (g) in [17], for (b) in [6], for (c) and (d) in [4], and for (e) and (f) in [1].”
Constructions of stable equivalences of Morita type for finite‐dimensional algebras III (2007, background): “Since a stable equivalence of Morita type preserves the finitistic and representation dimensions [23], the last property follows.”
On the finitistic dimension conjecture I: related to representation-finite algebras (2004, background): “For further new results on representation dimension we refer to [ 18 , 19].”
Representation dimension of exterior algebras (2006, background): “Various classes of algebras with representation dimension 3 have been found: algebras with radical square zero [Au, §III.5, Proposition p. 56], hereditary algebras [Au, §III.5, Proposition p. 58] and more generally stably hereditary algebras [ Xi , Theorem 3.5], special biserial algebras [ErHoIySc],”