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Cohomological Hall Algebras, Semicanonical Bases and Donaldson–Thomas Invariants for 2-dimensional Calabi–Yau Categories (with an Appendix by Ben Davison)

Part of the Progress in Mathematics book series (PM,volume 324)

Abstract

We discuss semicanonical bases from the point of view of Cohomological Hall algebras via the “dimensional reduction” from 3-dimensional Calabi–Yau categories to 2-dimensional ones. Also, we discuss the notion of motivic Donaldson–Thomas invariants (as defined by M. Kontsevich and Y. Soibelman) in the framework of 2-dimensional Calabi–Yau categories. In particular we propose a conjecture which allows one to define Kac polynomials for a 2-dimensional Calabi–Yau category (this is a theorem of S. Mozgovoy in the case of preprojective algebras).

Mathematics Subject Classification (2010).

  • 16G20
  • 14F42
  • 81R99

Keywords

  • Cohomological Hall algebras
  • motivic Donaldson–Thomas invariants
  • 2-dimensional Calabi–Yau categories
  • semicanonical bases

To Maxim Kontsevich on his 50th birthday

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Correspondence to Jie Ren .

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Ren, J., Soibelman, Y. (2017). Cohomological Hall Algebras, Semicanonical Bases and Donaldson–Thomas Invariants for 2-dimensional Calabi–Yau Categories (with an Appendix by Ben Davison). In: Auroux, D., Katzarkov, L., Pantev, T., Soibelman, Y., Tschinkel, Y. (eds) Algebra, Geometry, and Physics in the 21st Century. Progress in Mathematics, vol 324. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59939-7_7

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