On super cluster algebras based on super Plücker and super Ptolemy relations

We consider and compare super Plücker Ptolemy relations from the perspective of constructing cluster algebras. develop structure Grassmannians Gr2|0(n|1) for arbitrary n, which was indicated earlier in our joint work with Th. Voronov. also analyze “weighted projective” case obtain a new simple form Grr|1(n|1). To this end, we establish properties Berezinians certain type matrices (which call “wrong”). For relation decorated Teichmüller space Penner-Zeitlin, show how by change variables it can be transformed into classical even decoupled odd variables.