Abstract
AbstractAs 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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