Acyclic Cluster Algebras from a Ring Theoretic Point of View

Cluster Mutation via Quiver Representations

Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categories of hereditary algebras. Using this, we obtain a representation theoretic interpretation of cluster mutation in case of acyclic cluster algebras.

Fuzzy sets form A meta-system-theoretic point of view

0 on Cohen - Macaulay Rings of Invariants

We investigate the transfer of the Cohen-Macaulay property from a commutative ring to a subring of invariants under the action of a finite group. Our point of view is ring theoretic and not a priori tailored to a particular type of group action. As an illustration, we briefly discuss the special case of multiplicative actions, that is, actions on group algebras k[Z n ] via an action on Z n .

A fixed point method for proving the stability of ring $(alpha, beta, gamma)$-derivations in $2$-Banach algebras

In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(alpha, beta, gamma)$-derivations in $2$-Banach algebras.

On Homomorphisms from Ringel-hall Algebras to Quantum Cluster Algebras

In [1],the authors defined algebra homomorphisms from the dual RingelHall algebra of certain hereditary abelian categoryA to an appropriate q-polynomial algebra. In the case that A is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in [9]. Moreover, if the underlying graph of Q is bipartite and the matrix B associated t...