dc.contributor.author |
Ren, Jie |
|
dc.date.accessioned |
2017-08-14T16:54:08Z |
|
dc.date.available |
2017-08-14T16:54:08Z |
|
dc.date.issued |
2017-08-01 |
en_US |
dc.identifier.uri |
http://hdl.handle.net/2097/36260 |
|
dc.description.abstract |
The motivic Donaldson-Thomas theory of 2-dimensional Calabi-Yau categories can be induced from the theory of 3-dimensional Calabi-Yau categories via dimensional reduction. The cohomological Hall algebra is one approach to the motivic Donaldson-Thomas invariants. Given an arbitrary quiver one can construct a double quiver, which induces the preprojective algebra. This corresponds to a 2-dimensional Calabi-Yau category. One can further construct a triple quiver with potential, which gives rise to a 3-dimensional Calabi-Yau category. The critical cohomological Hall algebra (critical COHA for short) is defined for a quiver with potential. Via the dimensional reduction we obtain the cohomological Hall algebra (COHA for short) of the preprojective algebra. We prove that a subalgebra of this COHA consists of a semicanonical basis, thus is related to the generalized quantum groups. Another approach is motivic Hall algebra, from which an integration map to the quantum torus is constructed. Furthermore, a conjecture concerning some invariants of 2-dimensional Calabi-Yau categories is made.
We investigate the correspondence between the A∞-equivalent classes of ind-constructible 2-dimensional Calabi-Yau categories with a collection of generators and a certain type of quivers. This implies that such an ind-constructible category can be canonically reconstructed from its full subcategory consisting of the collection of generators. |
en_US |
dc.description.sponsorship |
National Science Fundation |
en_US |
dc.language.iso |
en_US |
en_US |
dc.publisher |
Kansas State University |
en |
dc.subject |
Cohomological Hall algebra |
en_US |
dc.subject |
2-dimensional Calabi-Yau category |
en_US |
dc.subject |
Quiver |
en_US |
dc.subject |
Semicanonical basis |
en_US |
dc.subject |
Donaldson-Thomas series |
en_US |
dc.title |
Cohomological Hall algebras and 2 Calabi-Yau categories |
en_US |
dc.type |
Dissertation |
en_US |
dc.description.degree |
Doctor of Philosophy |
en_US |
dc.description.level |
Doctoral |
en_US |
dc.description.department |
Department of Mathematics |
en_US |
dc.description.advisor |
Yan S. Soibelman |
en_US |
dc.date.published |
2017 |
en_US |
dc.date.graduationmonth |
August |
en_US |