Remarks on Cohomological Hall Algebras and Their Representations

  • Yan SoibelmanEmail author
Part of the Progress in Mathematics book series (PM, volume 319)


The aim of this paper is to discuss a class of representations of Cohomological Hall algebras related to the notion of framed stable object of a category. The paper is an extended version of the talk the author gave at the workshop on Donaldson–Thomas invariants at the University Paris-7 in June 2013 and at the conference “Algebra, Geometry, Physics” dedicated to Maxim Kontsevich (June 2014, IHES). Because of the origin of the paper it contains more speculations than proofs.


Modulus Space Central Charge Short Exact Sequence Abelian Category Lagrangian Submanifolds 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I thank Alexander Braverman, Emanuel Diaconescu, Sergei Gukov, Nigel Hitchin, Mikhail Kapranov, Gabriel Kerr, Melissa Liu, Hiraku Nakajima, Andy Neitzke, Alexei Oblomkov, Vivek Schende, Olivier Schiffmann, and Xinli Xiao for stimulating discussions and correspondences. I also thank the anonymous referee for multiple comments leading to the improvement of the paper. I am especially grateful to Maxim Kontsevich for numerous discussions on the subject of this paper and related projects. I also thank IHES for excellent research conditions. This work is partially supported by an NSF grant.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsKSUManhattanUSA

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