2,397 research outputs found
Covering functors without groups
Coverings in the representation theory of algebras were introduced for the
Auslander-Reiten quiver of a representation finite algebra by Riedtmann and
later for finite dimensional algebras by Bongartz and Gabriel, R.
Martinez-Villa and de la Pe\~na. The best understood class covering functors is
that of Galois covering functors F: A -> B determined by the action of a group
of automorphisms of A. In this work we introduce the balanced covering functors
which include the Galois class and for which classical Galois covering-type
results still hold. For instance, if F:A -> B is a balanced covering functor,
where A and B are linear categories over an algebraically closed field, and B
is tame, then A is tame.Comment: Some improvements have been made; in particular, the proof of Theorem
2 has been restructured and clarifie
On the number of terms in the middle of almost split sequences over cycle-finite artin algebras
We prove that the number of terms in the middle of an almost split sequence
in the module category of a cycle-finite artin algebra is bounded by 5
Walk entropies on graphs
Entropies based on walks on graphs and on their line-graphs are defined. They are based on the summation over diagonal and off-diagonal elements of the thermal Green’s function of a graph also known as the communicability. The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies. The temperature dependence of the walk entropies is also discussed. In particular, the walk entropy of graphs is shown to be non-monotonic for regular but non-walk-regular graphs in contrast to non-regular graphs
Optimal Control Realizations of Lagrangian Systems with Symmetry
A new relation among a class of optimal control systems and Lagrangian
systems with symmetry is discussed. It will be shown that a family of solutions
of optimal control systems whose control equation are obtained by means of a
group action are in correspondence with the solutions of a mechanical
Lagrangian system with symmetry. This result also explains the equivalence of
the class of Lagrangian systems with symmetry and optimal control problems
discussed in \cite{Bl98}, \cite{Bl00}.
The explicit realization of this correspondence is obtained by a judicious
use of Clebsch variables and Lin constraints, a technique originally developed
to provide simple realizations of Lagrangian systems with symmetry. It is
noteworthy to point out that this correspondence exchanges the role of state
and control variables for control systems with the configuration and Clebsch
variables for the corresponding Lagrangian system.
These results are illustrated with various simple applications
Periodic Coxeter matrices
AbstractLet A=kQ/I be a finite dimensional triangular k-algebra. Consider the Cartanmatrix CA and the Coxeter matrix ϕA=−CA−tCA. Let χϕ(T)=det(Tid−ϕA) be the Coxeter polynomial of A. We study conditions on SpecϕA in order that ϕA is a periodic matrix. We show that in case ϕA is periodic then the Euler quadratic form qA(x)=xCA−txt is non-negative and qA>0 if and only if 1∉SpecϕA
- …