What question did this study set out to answer?

The research aims to explicitly construct models of higher quantum groups using shifted Poisson structures.

March 28, 2026Open Access

Derived geometry and higher quantum groups

View Full Paper

Ask AI

Bookmark

Authors

This thesis reveals how shifted Poisson structures influence higher quantum groups, indicating new algebraic connections.

The research aims to explicitly construct models of higher quantum groups using shifted Poisson structures.
Developed graphical calculus for shifted Poisson structures in finitely generated algebras.
Characterized shifted Poisson structures via homotopy-coherent data and higher Lie algebras.
Studied infinitesimal deformations of symmetric monoidal structures in dg-categories.
Explored cases of 1, 2, 3, and 4-shifted Poisson structures in relation to higher quantum groups.
Recovered higher Lie quasibialgebras from the graphical calculus.
Showed that every 2-shifted Poisson structure leads to an infinitesimal 2-braiding.
Demonstrated obstructions to hexagon axioms at the second order of infinitesimal deformations.
Developed a framework for generating infinitesimal sylleptic deformations and their integrations.

Cameron Kemp (2026) studied this question.

View Full Paper

Ask AI

Bookmark