On super cluster algebras based on super Plücker and super Ptolemy relations
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909653138407424 |
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| author | Shemyakova, Ekaterina |
| author_facet | Shemyakova, Ekaterina |
| contents | We study super cluster algebra structure arising in examples provided by super Plücker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannians $\Gr_{2|0}(n|1)$ for arbitrary $n$, which was indicated earlier in our joint work with Th. Voronov. For the super Ptolemy relation for the decorated super Teichmüller 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 Plücker relations for general super Grassmannians and obtain a new simple form of the relations for $\Gr_{r|1}(n|1)$. To this end, we establish properties of Berezinians of certain type matrices (which we call ``wrong''). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_12072 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On super cluster algebras based on super Plücker and super Ptolemy relations Shemyakova, Ekaterina Mathematical Physics Combinatorics Differential Geometry We study super cluster algebra structure arising in examples provided by super Plücker and super Ptolemy relations. We develop the super cluster structure of the super Grassmannians $\Gr_{2|0}(n|1)$ for arbitrary $n$, which was indicated earlier in our joint work with Th. Voronov. For the super Ptolemy relation for the decorated super Teichmüller 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 Plücker relations for general super Grassmannians and obtain a new simple form of the relations for $\Gr_{r|1}(n|1)$. To this end, we establish properties of Berezinians of certain type matrices (which we call ``wrong''). |
| title | On super cluster algebras based on super Plücker and super Ptolemy relations |
| topic | Mathematical Physics Combinatorics Differential Geometry |
| url | https://arxiv.org/abs/2206.12072 |