## K-theoretic Hall algebras for quivers with potential

##### Author(s)

Pădurariu, Tudor(Tudor Gabriel)
Download1191267620-MIT.pdf (1.004Mb)

##### Other Contributors

Massachusetts Institute of Technology. Department of Mathematics.

##### Advisor

Davesh Maulik.

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Show full item record##### Abstract

Given a quiver with potential (Q, W), Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded algebra is supercommutative. A special case of this construction is related to work of Nakajima, Varagnolo, Maulik-Okounkov etc. about geometric constructions of Yangians and their representations; indeed, given a quiver Q, there exists an associated pair (Q̃, W̃) for which the CoHA is conjecturally the positive half of the Yangian Y[subscript MO]([subscript gQ]). The goal of this thesis is to extend these ideas to K-theory. More precisely, we construct a K-theoretic Hall algebra using category of singularities, define a filtration whose associated graded algebra is a deformation of a symmetric algebra, and compare the KHA and the CoHA using the Chern character. As before, we expect our construction for the special class of quivers (Q̃, W̃) to recover the positive part of quantum affine algebra U[subscript q]([subscript gQ]) defined by Okounkov-Smirnov, but for general pairs (Q, W) we expect new phenomena.

##### Description

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 Cataloged from the official PDF of thesis. Includes bibliographical references (pages 167-171).

##### Date issued

2020##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.