As is well known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plücker relations, Desnanot-Jacobi identities, and their generalizations. We present a construction that plays a similar role in a description of generalized cluster transformations and discuss its applications to generalized cluster structures in $GL n$ compatible with a certain subclass of Belavin-Drinfeld Poisson-Lie brackets, in the Drinfeld double of $GL n$, and in spaces of periodic difference operators.
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ASJC Scopus subject areas
- General Mathematics