Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for $2$-dimensional Calabi-Yau categories (with an appendix by Ben Davison)

Jie Ren; Yan Soibelman

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arXiv · 1508.06068

Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for $2$-dimensional Calabi-Yau categories (with an appendix by Ben Davison)

Jie Ren·Yan Soibelman

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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).

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BibTeX RIS

Jie Ren, Yan Soibelman. 2016-07-15. Cohomological Hall algebras, semicanonical bases and Donaldson-Thomas invariants for $2$-dimensional Calabi-Yau categories (with an appendix by Ben Davison). https://arxiv.org/abs/1508.06068

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