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Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for -dimensional Calabi-Yau categories (with an appendix by Ben Davison)
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).Comment: The revised version contains the Appendix written by Ben Davison
about the relationship of Kontsevich-Soibelman product with the one of
Schiffmann-Vassero
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