Related papers: Algebraic flows on commutative complex Lie groups
Starting from a higher Courant bracket associated to exceptional generalized geometry, we provide a systematic derivation of all types of fluxes and their Bianchi identities for four-dimensional compactifications of M-theory. We show that…
We study generalized Lie bialgebroids over a single point, that is, generalized Lie bialgebras. Lie bialgebras are examples of generalized Lie bialgebras. Moreover, we prove that the last ones can be considered as the infinitesimal…
In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical $R$-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie…
We consider the covering map $\pi:\mathbb{C}^n\to \mathbb{T}$ of a compact complex torus. Given an algebraic variety $X\subseteq \mathbb{C}^n$ we describe the topological closure of $\pi(X)$ in $\mathbb T$. We obtain a similar description…
We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…
In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \cite{UV} to the X-ray transform for a general flow.…
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
On a compact connected Lie group $G$, we study the global solvability and the cohomology spaces of the differential complex associated with an essentially real involutive structure that is invariant under left translations. We prove that…
W. Goldman and V. Turaev defined a Lie bialgebra structure on the $\mathbb Z$-module generated by free homotopy classes of loops of an oriented surface (i.e. the conjugacy classes of its fundamental group). We develop a generalization of…
All factorizable Lie bialgebra structures on complex reductive Lie algebras were described by Belavin and Drinfeld. We classify the symplectic leaves of the full class of corresponding connected Poisson-Lie groups. A formula for their…
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended…
We study the interplay between the diagonal flow on, and the topology of, a stratum component of a space of rooted quadratic differentials. We prove that the flow group -- the subgroup of the fundamental group generated by almost-flow loops…
We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…
We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite derivation subalgebra such that the commutative associative algebra is derivation-simple with…
We consider the space of $n$-tuples of pairwise commuting elements in the Lie algebra of $U(m)$. We relate its one-point compactification to the subquotients of certain rank filtrations of connective complex $K$-theory. We also describe the…
We provide a fundamental domain for the action of the finite Weyl group on a maximal torus of a compact Lie group of the corresponding type. The general situation is reduced to the adjoint case and, from the perspective of root data, this…
We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping bounded the length of the uniform current is compact (up to conjugation.) This implies that the spectrum of the length of…
We study the positive Hermitian curvature flow on the space of left-invariant metrics on complex Lie groups. We show that in the nilpotent case, the flow exists for all positive times and subconverges in the Cheeger-Gromov sense to a…
In this contributed presentation, we discuss and compare the mutually opposite procedures of deformations and contractions of Lie algebras. We suggest that with appropriate combinations of both procedures one may construct new Lie algebras.…