In this paper we propose the notion of cluster superalgebras which is a supersymmetric version of the classical cluster algebras introduced by Fomin and Zelevinsky. We show that the symplectic-orthogonal supergroup $SpO(2|1)$ admits a cluster superalgebra structure and as a consequence of this, we deduce that the supercommutative superalgebra generated by all the entries of a superfrieze is a subalgebra of a cluster superalgebra. We also show that the coordinate superalgebra of the super Grassmannian $G(2|0; 4|1)$ of chiral conformal superspace (that is, $(2|0)$ planes inside the superspace $\mathbb C^{4|1}$) is a quotient of a cluster superalgebra.
Li Li
1
;
James Mixco
2
;
B. Ransingh
3
;
Ashish K. Srivastava
2
1
Oakland University, Rochester, MI-48309, USA
2
Saint Louis University
3
Harish-Chandra Research Institute, India
Li Li; James Mixco; B. Ransingh; Ashish K. Srivastava. An introduction to supersymmetric cluster algebras. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/9442
@article{10_37236_9442,
author = {Li Li and James Mixco and B. Ransingh and Ashish K. Srivastava},
title = {An introduction to supersymmetric cluster algebras},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {1},
doi = {10.37236/9442},
zbl = {1467.13034},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9442/}
}
TY - JOUR
AU - Li Li
AU - James Mixco
AU - B. Ransingh
AU - Ashish K. Srivastava
TI - An introduction to supersymmetric cluster algebras
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/9442/
DO - 10.37236/9442
ID - 10_37236_9442
ER -
%0 Journal Article
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%A Ashish K. Srivastava
%T An introduction to supersymmetric cluster algebras
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/9442/
%R 10.37236/9442
%F 10_37236_9442
