Related papers: Post-Lie-Magnus expansion and BCH-recursion
The aim of this paper is twofold. In the first part, we consider twisted Rota-Baxter operators on associative algebras that were introduced by Uchino as a noncommutative analogue of twisted Poisson structures. We construct an…
Many features of classical Lie theory generalize to the broader context of algebras over Hopf operads. However, this idea remains largely to be developed systematically. Quasi-shuffle algebras provide for example an interesting illustration…
We use the octahedron recurrence to give a simplified statement and proof of a formula for iterated birational rowmotion on a product of two chains, first described by Musiker and Roby. Using this, we show that weights of certain chains in…
In this paper, we investigate the base-$p$ expansions of putative counterexamples to the $p$-adic Littlewood conjecture of de Mathan and Teuli\'e. We show that if a counterexample exists, then so does a counterexample whose base-$p$…
In this paper, we establish the Composition-Diamond lemma for associative nonunitary Rota-Baxter algebras with weight $\lambda$. As applications, we obtain a linear basis of a free commutative Rota-Baxter algebra without unity and show that…
The word problem for an arbitrary associative Rota-Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects, particularly of interest in physics, are…
We describe automorphisms, derivations, and Rota -- Baxter operators on the series of simple pre-Lie algebras found by D. Burde in 1998.
A relative Rota-Baxter operator on Lie 2-groups is introduced as a pair of relative Rota-Baxter operators on the underlying Lie groups which is also a Lie groupoid morphism. Such an operator induces a factorization theorem for Lie 2-groups…
In recent years, The BPHZ algorithm for renormalization in quantum field theory has been interpreted, after dimensional regularization, as the Birkhoff-(Rota-Baxter) decomposition (BRB) of characters on the Hopf algebra of Feynmann graphs,…
The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted…
We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$…
After the torch of Anders Kock [Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293], we will establish the Baker-Campbell-Hausdorff formula as well as the Zassenhaus formula in the…
We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the Weil-Petersson…
New algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This give the topological interpretation of the link invariants associated with the Weinstein--Xu classical solutions…
The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H=ln(e^X e^Y) for non-commuting X,Y. Formally H lives in the graded completion of the free Lie algebra L generated by X,Y. We present a…
The Bogoliubov recursion is a particular procedure appearing in the process of renormalization in perturbative quantum field theory. It provides convergent expressions for otherwise divergent integrals. We develop here a theory of…
We verify conjecture 5.11 of Panyushev [\emph{Antichains in weight posets associated with gradings of simple Lie algebras}, Math Z 281(3):1191--1214, 2015].
We obtain a complete time expansion of the pull-back operator generated by a real analytic flow of real analytic automorphisms acting on analytic tensor sections of a manifold. Our expansion is given in terms of multiple Lie derivatives.…
In geometry of nonlinear partial differential equations, recursion operators that act on symmetries of an equation $\mathcal{E}$ are understood as B\"{a}cklund auto-transformations of the equation $\mathcal{TE}$ tangent to $\mathcal{E}$. We…
By means of a generalization of the S-expansion method we construct a procedure to obtain expanded higher-order Lie algebras. It is shown that the direct product between an Abelian semigroup S and a higher-order Lie algebra…