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On cohomological and K-theoretical Hall algebras of symmetric quivers

par Lunts, Valery;Spenko, Špela ;Van den Bergh, Michel
Référence Journal of algebra, 639, page (440-463)
Publication Publié, 2024-02-01

Article révisé par les pairs

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Résumé :

We give a brief review of the cohomological Hall algebra CoHA H and the K-theoretical Hall algebra KHA R associated to quivers. In the case of symmetric quivers, we show that there exists a homomorphism of algebras (obtained from a Chern character map) R→Hˆσ˜ where Hˆσ˜ is a Zhang twist of the completion of H. Moreover, we establish the equivalence of categories of “locally finite” graded modules H-Modlf≃RQ-Modlf. Examples of locally finite Hˆ-, resp. RQ-modules appear naturally as the cohomology, resp. K-theory, of framed moduli spaces of quivers.