# The structure group for quasi-linear equations via universal enveloping algebras

@inproceedings{Linares2021TheSG, title={The structure group for quasi-linear equations via universal enveloping algebras}, author={Pablo Linares and Felix Otto and Markus Tempelmayr}, year={2021} }

We consider the approach of replacing trees by (fewer) multi-indices as an index set of the abstract model space T, which was introduced in [15] to tackle quasi-linear singular SPDE. We show that this approach is consistent with the postulates of regularity structures in [10] when it comes to the structure group G. In particular, G ⊂ Aut(T) arises from a Hopf algebra T and a comodule ∆: T → T ⊗ T. In fact, this approach, where the dual T of the abstract model space T naturally embeds into a…

## 4 Citations

A priori bounds for quasi-linear SPDEs in the full sub-critical regime

- Mathematics
- 2021

This paper is concerned with quasi-linear parabolic equations driven by an additive forcing ξ ∈ C, in the full subcritical regime α ∈ (0, 1). We are inspired by Hairer’s regularity structures,…

A diagram-free approach to the stochastic estimates in regularity structures

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- 2021

In this paper, we explore the version of Hairer’s regularity structures based on a greedier index set than trees, as introduced in [32] and algebraically characterized in [30]. More precisely, we…

Smooth rough paths, their geometry and algebraic renormalization

- Mathematics
- 2021

We introduce the class of “smooth rough paths” and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects.…

The Sewing lemma for $0<\gamma \leq 1$

- Mathematics
- 2021

We establish a Sewing lemma in the regime γ ∈ (0, 1], constructing a Sewing map which is neither unique nor canonical, but which is nonetheless continuous with respect to the standard norms. Two…

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