Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras

Fan Xu; Haicheng Zhang

Czechoslovak Mathematical Journal (2021)

  • Issue: 1, page 253-267
  • ISSN: 0011-4642

Abstract

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Let 𝒜 be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of 𝒜 via its derived Hall algebra and Bridgeland’s Hall algebra of m -cyclic complexes.

How to cite

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Xu, Fan, and Zhang, Haicheng. "Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras." Czechoslovak Mathematical Journal (2021): 253-267. <http://eudml.org/doc/297067>.

@article{Xu2021,
abstract = {Let $\{\mathcal \{A\}\}$ be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of $\{\mathcal \{A\}\}$ via its derived Hall algebra and Bridgeland’s Hall algebra of $m$-cyclic complexes.},
author = {Xu, Fan, Zhang, Haicheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {Heisenberg double; Drinfeld double; derived Hall algebra; Bridgeland's Hall algebra},
language = {eng},
number = {1},
pages = {253-267},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras},
url = {http://eudml.org/doc/297067},
year = {2021},
}

TY - JOUR
AU - Xu, Fan
AU - Zhang, Haicheng
TI - Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 253
EP - 267
AB - Let ${\mathcal {A}}$ be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of ${\mathcal {A}}$ via its derived Hall algebra and Bridgeland’s Hall algebra of $m$-cyclic complexes.
LA - eng
KW - Heisenberg double; Drinfeld double; derived Hall algebra; Bridgeland's Hall algebra
UR - http://eudml.org/doc/297067
ER -

References

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