Cohomological Hall algebras and 2 Calabi-Yau categories
dc.contributor.author | Ren, Jie | |
dc.date.accessioned | 2017-08-14T16:54:08Z | |
dc.date.available | 2017-08-14T16:54:08Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2017-08-01 | en_US |
dc.date.published | 2017 | en_US |
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.advisor | Yan S. Soibelman | en_US |
dc.description.degree | Doctor of Philosophy | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Doctoral | en_US |
dc.description.sponsorship | National Science Fundation | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/36260 | |
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 |