Tilted string algebras
François Huard,Shiping Liu +1 more
TL;DR: In this article, the authors find some simple combinatorial criteria for a string algebra to be tilted or quasi-tilt, which will enable one to construct a lot of new examples of tilted algebras.
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About: This article is published in Journal of Pure and Applied Algebra. The article was published on 25 Oct 2000. and is currently open access. The article focuses on the topics: String (computer science) & Simple (abstract algebra).
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Citations
Gentle algebras arising from surface triangulations
TL;DR: In this paper, the authors associate an algebra A(Γ) to a triangulation Γ of a surface S with a set of boundary marking points, and prove that the algebra is cluster-tilted if and only if the surface S is a disc or an annulus.
On the First Hochschild Cohomology Group of a Cluster-Tilted Algebra
TL;DR: In this article, the first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B is studied, and it is shown that if B is tame, then HH1B is isomorphic, as a k-vector space, to the direct sum of \({\text {HH}}^{1}(C) with \(nB,C) where nB,c is an invariant linking the bound quivers of B and C.
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•Posted Content
On the first Hochschild cohomology group of a cluster-tilted algebra
TL;DR: In this paper, the first Hochschild cohomology group with coefficients in the B-B-bimodule B is studied, and it is shown that if C is constrained, or if B is tame, then HH^1(B) is isomorphic, as a k-vector space, to the direct sum of HH^ 1(C) with k ∆, where n ∆ is an invariant linking the bound quivers of B and C.
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References
Triangulated Categories in the Representation of Finite Dimensional Algebras
Dieter Happel
- 11 Feb 1988
TL;DR: The use of triangulated categories in the study of representations of finite-dimensional algebras has been studied extensively in the literature as discussed by the authors, and triangulation is a useful tool in studying tilting processes.
1.9K
•Book
Tame Algebras and Integral Quadratic Forms
Claus Michael Ringel
- 01 Dec 1984
TL;DR: In this article, the construction of stable separating tubular families and tubular algebras are discussed. But they do not discuss the relation between tubular extensions and directed algesbras.
1.7K
•Book
Tilting in Abelian Categories and Quasitilted Algebras
Dieter Happel,Idun Reiten,O SmaløSverre +2 more
- 01 Jan 1996
797
Auslander-reiten sequences with few middle terms and applications to string algebrass
TL;DR: In this paper, the Auslander-reiten sequences with few middle terms and applications to string algebras are presented. But they do not have any application to string algebra.