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Lower bound cluster algebras: presentations, Cohen–Macaulayness, and normality
Muller, Greg1; Rajchgot, Jenna2; Zykoski, Bradley3
1 University of Oklahoma
2 University of Saskatchewan
3 University of Michigan
Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 95-114.

We give an explicit presentation for each lower bound cluster algebra. Using this presentation, we show that each lower bound algebra Gröbner degenerates to the Stanley–Reisner scheme of a vertex-decomposable ball or sphere, and is thus Cohen–Macaulay. Finally, we use Stanley–Reisner combinatorics and a result of Knutson–Lam–Speyer to show that all lower bound algebras are normal.

Received:
Accepted:
Published online:
DOI: 10.5802/alco.2
Classification: 13F60, 05E40, 13F55
Keywords: Cluster algebras, lower bound cluster algebras, combinatorial commutative algebra, Stanley–Reisner complexes

Muller, Greg 1; Rajchgot, Jenna 2; Zykoski, Bradley 3

1 University of Oklahoma
2 University of Saskatchewan
3 University of Michigan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Muller, Greg; Rajchgot, Jenna; Zykoski, Bradley. Lower bound cluster algebras: presentations, Cohen–Macaulayness, and normality. Algebraic Combinatorics, Volume 1 (2018) no. 1, pp. 95-114. doi : 10.5802/alco.2. https://alco.centre-mersenne.org/articles/10.5802/alco.2/

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