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International Workshop on Cluster Algebras and Related Topics
International Workshop Cluster Algebras and Related Topics
2017/2/15
The purposes of this conference are to discuss the structures and classifications of the cluster algebras of geometric type, the recent advances of several main conjectures of cluster theory, the conn...
Twisted split category algebras as quasi-hereditary algebras
Group Theory category algebras quasi-hereditary algebras
2012/4/16
A category is called {\em split} if for every morphism $s\colon X\to Y$ there exists a morphism $t\colon Y\to X$ such that $s\circ t\circ s = s$. Let $C$ be a finite split category, let $k$ be a field...
Free group algebras in Malcev-Neumann skew fields of fractions
Division rings Malcev-Neumann series Rings and Algebras
2011/9/5
Abstract: Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free gro...
Random partitions and asymptotic theory of symmetric groups, Hecke algebras and finite Chevalley groups
Random partitions asymptotic theory of symmetric groups Hecke algebras finite Chevalley groups
2011/2/22
Kit meanwhile had begun to frequent the Applied Mechanics Institute. Since Prandtl’s recent discovery of the boundary layer, things over there had been hopping, with intense inquiry into matters of li...
The purpose of this chapter is to give an introduction to the theory of cluster categories and cluster-tilted algebras, with some background on the theory of cluster algebras, which motivated these to...
Mathieu Subspaces of Univariate Polynomial Algebras
Mathieu subspaces the (Strong) Image Conjecture the (Strong) Integral Conjecture
2011/1/20
We first give a characterization for Mathieu subspaces of univariate polynomial algebras over fields in terms of their radicals.We then deduce that for some classes of classical univariate
orthogonal...
Conjugacy classes in Weyl groups and q-W algebras
Conjugacy classes Weyl groups q-W algebras
2010/11/17
We define noncommutative deformations W_q^s(G) of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group G which play the role of Slodowy sl...
Analogue of the Duistermaat-van der Kallen Theorem for Group Algebras
Duistermaat-van der Kallen Theorem Mathieu subspaces
2010/12/14
Let G be a group, R an integral domain, and VG the R-subspace of the group algebra R[G] consisting of all the elements of R[G] whose coefficient of the identity element 1G of G is equal to zero.
The algebras derived equivalent to gentle cluster tilted algebras
gentle algebras cluster tilted algebras derived equiva equivalence
2010/11/30
A cluster tilted algebra is known to be gentle if and only if it is cluster tilted of Dynkin type A or Euclidean type ˜A . We classify all finite dimensional algebras which are derived equivalent...
Cluster algebras and representation theory
cluster algebra canonical and semicanonical basis preprojective algebra
2010/12/10
We apply the new theory of cluster algebras of Fomin and Zelevinsky to study some combinatorial problems arising in Lie theory. This is joint work with Geiss and Schr¨oer (§3, 4, 5, 6), and with Herna...
This paper investigates the Poisson geometry associate to a cluster algebra over the complex numbers, and its relationship to compatible torus actions.