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Pré-Publication, Document De Travail Année : 2015

Quantum Grothendieck rings and derived Hall algebras

David Hernandez
Bernard Leclerc

Résumé

We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain an isomorphism with the derived Hall algebra of the derived category of a quiver Q of the same Dynkin type. Along the way, we study for each choice of orientation Q a tensor subcategory whose t-deformed Grothendieck ring is isomorphic to the positive part of a quantum enveloping algebra of the same Dynkin type, where the classes of simple objects correspond to Lusztig's dual canonical basis.
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hal-00797845 , version 1 (27-02-2024)

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David Hernandez, Bernard Leclerc. Quantum Grothendieck rings and derived Hall algebras. 2013. ⟨hal-00797845⟩
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