Zobrazeno 1 - 10
of 1 392
pro vyhledávání: '"13F60"'
Autor:
Pompili, Mara
We determine the class group of those generalized cluster algebras that are Krull domains. In particular, this provides a criterion for determining whether or not a generalized cluster algebra is a UFD. In fact, any finitely generated abelian group c
Externí odkaz:
http://arxiv.org/abs/2411.14963
Autor:
Grabowski, Jan E., Pressland, Matthew
We develop a general theory of cluster categories, applying to a 2-Calabi-Yau extriangulated category $\mathcal{C}$ and cluster-tilting subcategory $\mathcal{T}$ satisfying only mild finiteness conditions. We show that the structure theory of $\mathc
Externí odkaz:
http://arxiv.org/abs/2411.11633
Machine learning (ML) has emerged as a powerful tool in mathematical research in recent years. This paper applies ML techniques to the study of quivers--a type of directed multigraph with significant relevance in algebra, combinatorics, computer scie
Externí odkaz:
http://arxiv.org/abs/2411.04209
Autor:
Contu, Alessandro
Using Hernandez-Leclerc's isomorphism between the derived Hall algebra of a representation-finite quiver $Q$ and the quantum Grothendieck ring of the quantum loop algebra of the Dynkin type of $Q$, we lift the (quantum) cluster algebra structure of t
Externí odkaz:
http://arxiv.org/abs/2410.18604
Autor:
Lin, Mingyan Simon
We derive the cluster structure on the conjugation quotient Coxeter double Bruhat cells of a simple Lie group from that on the double Bruhat cells of the corresponding adjoint Lie group given by Fock and Goncharov using the notion of amalgamation giv
Externí odkaz:
http://arxiv.org/abs/2410.17568
Autor:
De Loera, Javier
For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weight
Externí odkaz:
http://arxiv.org/abs/2410.14554
Autor:
Felikson, Anna, Tumarkin, Pavel
We provide a classification of positive integral friezes on marked bordered surfaces. The classification is similar to the Conway--Coxeter's one: positive integral friezes are in one-to-one correspondence with ideal triangulations supplied with a col
Externí odkaz:
http://arxiv.org/abs/2410.13511
This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a $T$-path formula expressing the Laurent phenomenon, an
Externí odkaz:
http://arxiv.org/abs/2410.13507
Autor:
Fujita, Ryo
We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by Nakajima
Externí odkaz:
http://arxiv.org/abs/2410.10070
Autor:
Liu, Siyang, Pan, Jie
We describe the conjugation of the reddening sequence according to the formula of $c$-vectors with respect to changing of the initial seed. As applications, we extend the Rotation Lemma, the Target before Source Theorem, and the mutation invariant pr
Externí odkaz:
http://arxiv.org/abs/2410.09585