Deformations of group actions

Deformations of Group Actions

Let G be a noncompact real algebraic group and Γ < G a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of G or Γ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when G = SO(1, n) and provide a simple proof that any action of a compact Lie group is locally rigid.

Quantum Group Actions, Twisting Elements, and Deformations of Algebras

We construct twisting elements for module algebras of restricted two-parameter quantum groups from factors of their R-matrices. We generalize the theory of Giaquinto and Zhang to universal deformation formulas for categories of module algebras and give examples arising from R-matrices of two-parameter quantum groups.

First Cohomology, Rigidity and Deformations of Isometric Group Actions

In 1964, Weil gave a criterion for local rigidity of a homomorphism from a finitely generated group Γ to a finite dimensional Lie group G in terms of cohomology of Γ with coefficients in the Lie algebra of G. This note announces a generalization of Weil’s result to a class of homomorphisms into certain infinite dimensional Lie groups, namely diffeomorphism groups of compact manifolds. This give...

Mixed Braid Group Actions from Deformations of Surface Singularities

We consider a set of toric Calabi–Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group...

Actions on Manifolds from Deformations