Results 51 to 60 of about 2,837 (110)

ABHY Associahedra and Newton polytopes of F$F$‐polynomials for cluster algebras of simply laced finite type

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract A new construction of the associahedron was recently given by Arkani‐Hamed, Bai, He, and Yan in connection with the physics of scattering amplitudes. We show that their construction (suitably understood) can be applied to construct generalized associahedra of any simply laced Dynkin type.
Véronique Bazier‐Matte, Nathan Chapelier‐Laget, Guillaume Douville, Kaveh Mousavand, Hugh Thomas, Emine Yildirim   +5 more
wiley   +1 more source

On wings of the Auslander–Reiten quivers of selfinjective algebras [PDF]

Colloquium Mathematicum, 2005
Summary: We give necessary and sufficient conditions for a wing of an Auslander-Reiten quiver of a selfinjective algebra to be the wing of the radical of an indecomposable projective module. Moreover, a characterization of indecomposable Nakayama algebras of Loewy length~\(\geq 3\) is obtained.
Kwiecień, Marta, Skowroński, Andrzej
openaire   +1 more source

Grassmannians and Cluster Structures. [PDF]

Bull Iran Math Soc, 2021
Baur K.
europepmc   +1 more source

Equivariant multiplicities via representations of quantum affine algebras. [PDF]

Sel Math New Ser, 2023
Casbi E, Li JR.
europepmc   +1 more source

Consequences of the existence of Auslander-Reiten triangles with applications to perfect complexes for self-injective algebras

, 2013
In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them.
Webb, Peter
core  

Components of Auslander-Reiten Quivers with Only Preprojective Modules

Journal of Algebra, 1993
If \(A\) is an Artin algebra, a connected component \({\mathcal C}\) of its Auslander-Reiten quiver \(\Gamma_ A\) is a \(\pi\)-component if all indecomposables in \({\mathcal C}\) are preprojective in the sense of \textit{M. Auslander} and \textit{S. O. Samlø} [see J. Algebra 66, 61-122 (1980; Zbl 0477.16013)].
openaire   +2 more sources

On the vertices of modules in the Auslander–Reiten quiver III

Advanced Studies in Pure Mathematics, 1994
Let \(kG\) be the group algebra of a finite group \(G\) over a perfect field \(k\) of characteristic \(p\), and let \(\Gamma\) be a connected component of the stable Auslander-Reiten quiver of \(kG\). This is a continuation of part I [ibid. 208, No. 3, 411-436 (1991; Zbl 0725.20015)] written by the second author. It improves the result of its theorem A
Uno, Katsuhiro, Okuyama, Tetsuro
openaire   +3 more sources

On periodic stable Auslander-Reiten components containing Heller lattices over the symmetric Kronecker algebra

, 2018
Let $\mathcal{O}$ be a complete discrete valuation ring, $\mathcal{K}$ its quotient field, and let $A$ be the symmetric Kronecker algebra over $\mathcal{O}$. We consider the full subcategory of the category of $A$-lattices whose objects are $A$-lattices $
Miyamoto, Kengo
core  

On modules with cyclic vertices in the Auslander-Reiten quiver

Journal of Algebra, 1986
Let M be an indecomposable, non-projective module belonging to a block B of non-cyclic defect of a modular group algebra in odd characteristic. If \(\to \tau M\to E\to M\to 0\) is the Auslander-Reiten sequence, then E is indecomposable and non-projective. In the parlance of \textit{C. M. Ringel} [Tame algebras and integral quadratic forms (Lect.
openaire   +2 more sources

Auslander-Reiten triangles and quivers over topological spaces

, 2003
In this paper, Auslander-Reiten triangles are introduced into algebraic topology, and it is proved that their existence characterizes Poincare duality spaces. Invariants in the form of quivers are also introduced, and Auslander-Reiten triangles and quivers over spheres are computed.
openaire   +2 more sources