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arXiv · 1504.06758

Companion cluster algebras to a generalized cluster algebra

Tomoki Nakanishi·Dylan Rupel
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Abstract

We study the $c$-vectors, $g$-vectors, and $F$-polynomials for generalized cluster algebras satisfying a normalization condition and a power condition recovering classical recursions and separation of additions formulas. We establish a relationship between the $c$-vectors, $g$-vectors, and $F$-polynomials of such a generalized cluster algebra and its (left- and right-) companion cluster algebras. Our main result states that the cluster variables and coefficients of the (left- and right-) companion cluster algebras can be recovered via a specialization of the $F$-polynomials.

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Tomoki Nakanishi, Dylan Rupel. 2015-04-25. Companion cluster algebras to a generalized cluster algebra. https://arxiv.org/abs/1504.06758

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