scholarly journals Strongness of companion bases for cluster-tilted algebras of finite type

2018 ◽  
Vol 146 (6) ◽  
pp. 2409-2416
Author(s):  
Karin Baur ◽  
Alireza Nasr-Isfahani
Keyword(s):  
Finite Type ◽  
Tilted Algebras

Open Frobenius Cluster-Tilted Algebras

2022 ◽  
Vol 29 (01) ◽  
pp. 1-22
Author(s):  
Viviana Gubitosi
Keyword(s):  
Finite Type ◽  
Tilted Algebra ◽  
Frobenius Structures ◽  
Tilted Algebras ◽  
Cluster Tilted Algebra

In this paper, we compute the Frobenius dimension of any cluster-tilted algebra of finite type. Moreover, we give conditions on the bound quiver of a cluster-tilted algebra [Formula: see text] such that [Formula: see text] has non-trivial open Frobenius structures.

Finite Repetitive Generalized Cluster Complexes and d-Cluster Categories

2013 ◽  
Vol 20 (01) ◽  
pp. 123-140
Author(s):  
Teng Zou ◽  
Bin Zhu
Keyword(s):  
Simplicial Complex ◽  
Root System ◽  
Cluster Complex ◽  
Cluster Complexes ◽  
Endomorphism Algebras ◽  
Tilted Algebras ◽  
Cluster Categories ◽  
Hereditary Algebras ◽  
Cluster Tilting ◽  
Tilting Objects

For any positive integer n, we construct an n-repetitive generalized cluster complex (a simplicial complex) associated with a given finite root system by defining a compatibility degree on the n-repetitive set of the colored root system. This simplicial complex includes Fomin-Reading's generalized cluster complex as a special case when n=1. We also introduce the intermediate coverings (called generalized d-cluster categories) of d-cluster categories of hereditary algebras, and study the d-cluster tilting objects and their endomorphism algebras in those categories. In particular, we show that the endomorphism algebras of d-cluster tilting objects in the generalized d-cluster categories provide the (finite) coverings of the corresponding (usual) d-cluster tilted algebras. Moreover, we prove that the generalized d-cluster categories of hereditary algebras of finite representation type provide a category model for the n-repetitive generalized cluster complexes.

ON FINITE TYPE 3-MANIFOLD INVARIANTS I

1996 ◽  
Vol 05 (04) ◽  
pp. 441-461 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Vector Space ◽  
Finite Type ◽  
Commutative Algebra ◽  
Integral Homology ◽  
Knot Invariants ◽  
Finite Type Invariants ◽  
Definition Of ◽  
Type 3

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.

Perturbations of multidimensional shifts of finite type

2010 ◽  
Vol 31 (2) ◽  
pp. 483-526 ◽  
Author(s):  
RONNIE PAVLOV
Keyword(s):  
Finite Type ◽  
Lower Bounds ◽  
Symbolic Dynamics ◽  
Upper And Lower Bounds ◽  
Shift Of Finite Type ◽  
Strongly Irreducible ◽  
Dimensional Cube

AbstractIn this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any ℤd shift of finite type X with d>1 and any finite pattern w in the language of X, we denote by Xw the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on htop (X)−htop (Xw) dependent on the size of w. This extends a result of Lind for d=1 . We also apply our methods to an undecidability question in ℤd symbolic dynamics.

Ruled submanifolds with finite type Gauss map

1994 ◽  
Vol 49 (1-2) ◽  
pp. 42-45 ◽  
Author(s):  
Christos Baikoussis
Keyword(s):  
Finite Type ◽  
Gauss Map
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