# Yangians from cohomological Hall algebras

### APA

Davison, B. (2019). Yangians from cohomological Hall algebras. Perimeter Institute. https://pirsa.org/19020057

### MLA

Davison, Ben. Yangians from cohomological Hall algebras. Perimeter Institute, Feb. 26, 2019, https://pirsa.org/19020057

### BibTex

@misc{ pirsa_PIRSA:19020057, doi = {10.48660/19020057}, url = {https://pirsa.org/19020057}, author = {Davison, Ben}, keywords = {Mathematical physics}, language = {en}, title = {Yangians from cohomological Hall algebras}, publisher = {Perimeter Institute}, year = {2019}, month = {feb}, note = {PIRSA:19020057 see, \url{https://pirsa.org}} }

University of Edinburgh

Talk Type

**Subject**

Abstract

I will explain various features of the preprojective CoHA, a kind of universal algebra of correspondences generalising the algebras of endomorphisms of cohomology of quiver varieties considered by Nakajima. In particular I will focus on features of this algebra that become visible after viewing it as a dimensional reduction of the Kontsevich-Soibelman) critical CoHA associated to a related 3-dimensional Calabi-Yau category. Many nice features emerge from this view, e.g. an embedding in a related shuffle algebra, a formula for the graded dimension of the algebra, a flat non cocommutative deformation, a cocommutative coproduct, a geometric doubling procedure, the PBW theorem, an isomorphism with the Yangian considered by Maulik and Okounkov... I will focus on the perverse filtration, which is the key feature of my joint work with Sven Meinhardt, and gives rise to most of the above