On super cluster algebras based on super Pl\"ucker and super Ptolemy relations
Mathematical Physics
2025-06-23 v2 Combinatorics
Differential Geometry
math.MP
Abstract
We study super cluster algebra structure arising in examples provided by super Pl\"{u}cker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannians for arbitrary , which was indicated earlier in our joint work with Th. Voronov. For the super Ptolemy relation for the decorated super Teichm\"{u}ller space of Penner-Zeitlin, we show how by a change of variables it can be transformed into the classical Ptolemy relation with the new even variables decoupled from odd variables. We also analyze super Pl\"{u}cker relations for general super Grassmannians and obtain a new simple form of the relations for . To this end, we establish properties of Berezinians of certain type matrices (which we call ``wrong'').
Keywords
Cite
@article{arxiv.2206.12072,
title = {On super cluster algebras based on super Pl\"ucker and super Ptolemy relations},
author = {Ekaterina Shemyakova},
journal= {arXiv preprint arXiv:2206.12072},
year = {2025}
}