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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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Defining cluster algebras of finite type $\mathrm{A}$ by generators and relations
Consider a cluster algebra of finite type $\mathrm{A}$. The set of all (distinct) cluster variables is of finite cardinality, denote it by $k$, for such algebra. Is it true that, for an arbitrary choi …
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About cluster variables obtained by (sequentially) mutating at exchangeable variables from a...
Let $\Sigma=(X,ex,B)$ be a seed, $\mathcal{A}(\Sigma)$ a corresponding geometric cluster algebra and $\mathcal{X}_{\Sigma}$ the set of all cluster variables of $\mathcal{A}(\Sigma)$. We call a sequenc …