Radical embeddings and representation dimension
By K. Erdmann, Thorsten Holm, Osamu Iyama, J. Schröer. 2002
138 citations recorded by the source corpus.
Given a representation-finite algebra B and a subalgebra A of B such that the Jacobson radicals of A and B coincide, we prove that the representation dimension of A is at most three. By a result of Igusa and Todorov, this implies that the finitistic dimension of A is finite.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f6e0dfc886da58e06480e971085dbfb632d83128
How researchers see this paper
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In Algebra and Number Theory
- Jiaqun Wei
- Osamu Iyama
- Changchang Xi
- Gustavo Jasso
- Peter Jørgensen
- B. Keller
- I. Reiten
- Steffen Oppermann
In Discrete Mathematics and Combinatorics
- Changchang Xi
- Osamu Iyama
- Jiaqun Wei
- Gustavo Jasso
- B. Keller
- Lidia Angeleri Hugel
- Aslak Bakke Buan
- David Pauksztello
In Geometry and Topology
- Jiaqun Wei
- Osamu Iyama
- Changchang Xi
- Gustavo Jasso
- B. Keller
- Peter Jørgensen
- I. Reiten
- Lidia Angeleri Hugel
Citations in the corpus
- 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].”
- On the finitistic dimension conjecture, III: Related to the pair eAe⊆A (2008, methodology): “For a proof of this fact, we refer to [2,10, 12 ,31] and [19].”
- On the finitistic dimension conjecture I: related to representation-finite algebras (2004, methodology): “Note also that the proofs in [ 4 ] do not extend to our cases of (3) and (2).”
- Auslander–Reiten theory revisited (2008, background): “A lot of interesting results are known recently (see [120, 57]).”