Work

Periodic Staircase Matrices and Generalized Cluster Structures

Year: 2020

Type: article

Abstract: 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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaa148

Authors: Misha Gekhtman, Michael Shapiro, Alek Vainshtein

Institutions: University of Notre Dame, Michigan State University, University of Haifa

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Israel Science Foundation

Awards: Collaborative Research: Generalized Cluster Structures of Geometric Type, Collaborative Research: Generalized Cluster Structures of Geometric Type, G8432088075