Related papers: Bistellar Cluster Algebras and Piecewise Linear In…
The spaces of triangulations of a given manifold have been widely studied. The celebrated theorem of Pachner~\cite{Pachner} says that any two triangulations of a given manifold can be connected by a sequence of bistellar moves, or Pachner…
We define an operation which associates to a pair (B,M) where B is a cluster-tilted algebra and M is a B-module which lies in a local slice of B, a new cluster-tilted algebra B'. In terms of the quivers, this operation corresponds to adding…
Division algebras have demonstrated their utility in studying non-associative algebras and their connection to the Standard Model through complex Clifford algebras. This article focuses on exploring the connection between these complex…
Using cluster tilting theory, we investigate tilting objects in the stable category of vector bundles on a weighted projective line of weight type $(2, 2, 2, 2)$. More precisely, a tilting object consisting of rank-two bundles is…
We conclude the construction of the algebraic complex, consisting of spaces of differentials of Euclidean metric values, for four-dimensional piecewise-linear manifolds. Assuming that the complex is acyclic, we investigate how its torsion…
We consider the diffeological version of the Clifford algebra of a (diffeological) finite-dimensional vector space; we start by commenting on the notion of a diffeological algebra (which is the expected analogue of the usual one) and that…
In the study of induced bilinear systems, the classical Lie algebra rank condition (LARC) is known to be impractical since it requires computing the rank everywhere. On the other hand, the transitive Lie algebra condition, while more…
Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of…
We introduce a new class of finite dimensional gentle algebras, the surface algebras, which are constructed from an unpunctured Riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary…
In association with a finite dimensional algebra A of global dimension two, we consider the endomorphism algebra of A, viewed as an object in the triangulated hull of the orbit category of the bounded derived category, in the sense of…
We give a precise definition of folded quivers and folded cluster algebras. We give many examples of including some with finite mutation structure that do not have analogues in the unfolded cases. We relate these examples to the finite…
We introduce admissible group actions on cluster algebras, cluster categories and quivers with potential and study the resulting orbit spaces. The orbit space of the cluster algebra has the structure of a generalized cluster algebra. This…
Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied.…
The purpose of the present article is to define and study a new class of descent algebras, called twisted descent algebras. These algebras are associated to the Barratt-Joyal theory of twisted bialgebras in the same way than classical…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely…
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…
We construct a universal continuous invariant bilinear form for the Lie algebra of compactly supported sections of a Lie algebra bundle in a topological sense. Moreover we construct a universal continuous central extension of a current…
A prototypical examples of a cluster algebra is the coordinate ring of a finite Grassmannian: using the Pl\"ucker embedding the cluster algebra structure allows one to move between `maximal sets' of algebraically independent Pl\"ucker…
We generalize Jones' planar algebras by internalising the notion to a pivotal braided tensor category $\mathcal{C}$. To formulate the notion, the planar tangles are now equipped with additional `anchor lines' which connect the inner circles…