What is a post-Lie algebra and why is it useful in geometric integration

Abstract

We explain the notion of a post-Lie algebra and outline its role in the theory of Lie group integrators.

References in corpus (8)

• Homology of generalized partition posets
• Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras
• On post-Lie algebras, Lie--Butcher series and moving frames
• Pre-Lie algebras and the rooted trees operad
• On the Lie enveloping algebra of a post-Lie algebra
• Post-Lie algebras and factorization theorems
• Post-Lie Algebras and Isospectral Flows
• Hopf-algebraic structures of families of trees

Cited by in corpus (13)

• GPU-Acceleration of the ELPA2 Distributed Eigensolver for Dense Symmetric and Hermitian Eigenproblems
• A neural network multigrid solver for the Navier-Stokes equations
• Kernel methods for center manifold approximation and a data-based version of the Center Manifold Theorem
• High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem
• A $\mu$-mode integrator for solving evolution equations in Kronecker form
• $3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras
• Reduced basis stabilization and post-processing for the virtual element method
• Splitting-based domain decomposition methods for two-phase flow with different rock types
• Global random walk solvers for reactive transport and biodegradation processes in heterogeneous porous media
• Multidimensional smoothness indicators for first-order Hamilton-Jacobi equations
• Automated solver selection for simulation of multiphysics processes in porous media
• Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization
• Left-symmetric superalgebras and Lagrangian extensions of Lie superalgebras in characteristic 2