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).
To Maxim Kontsevich on his 50th birthday
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-59939-7_7
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-59938-0
Online ISBN: 978-3-319-59939-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)