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Generalized cluster structure on the Drinfeld double of \(\mathrm{GL}_n\). (Structures d’algébres amassées généralisées sur le double de Drinfeld du group \(\mathrm{GL}_n\).) (English. French summary) Zbl 1387.13047
Summary: We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson-Lie group \(\mathrm{GL}_n\) and derive from it a generalized cluster structure in \(\mathrm{GL}_n\) compatible with the push-forward of the dual Poisson-Lie bracket.

13F60 Cluster algebras
17B62 Lie bialgebras; Lie coalgebras
Full Text: DOI
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