Related papers: Higher Lie algebra actions on Lie algebroids
We define and make initial study of Lie groupoids equipped with a compatible homogeneity (or graded bundle) structure, such objects we will refer to as weighted Lie groupoids. One can think of weighted Lie groupoids as graded manifolds in…
In this paper we study Zimmer's conjecture for $C^1$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the…
We look at two examples of homotopy Lie algebras (also known as L_{\infty} algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree…
The equations for the critical points of the action functional defined by a Lagrangian depending on higher-order derivatives of admissible curves on a Lie algebroid are found. The relation with Euler-Poincar\'e and Lagrange Poincar\'e type…
We study actions by higher-rank abelian groups on quotients of semisimple Lie groups with finite center. First, we consider actions arising from the flows of two commuting elements of the Lie algebra--one nilpotent, and the other…
If P is a dg-operad acting on a dg-algebra A via algebra homomorphisms, then P acts on the Hochschild complex of A. In the more general case when P is a dg-prop, we show that P still acts on the Hochschild complex, but only up to coherent…
We classify the transitive, effective, holomorphic actions of connected complex Lie groups on complex surfaces.
Poisson actions of Poisson Lie groups have an interesting and rich geometric structure. We will generalize some of this structure to Dirac actions of Dirac Lie groups. Among other things, we extend a result of Jiang-Hua-Lu, which states…
In this paper we consider deformations of an algebroid stack on an etale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions…
In this paper, we focus on how we can interpret the actions of the elements in the Gelfand spectrum of a weighted Fourier algebra on connected Lie groups. They can be viewed as evaluations on specific points of the complexification of the…
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…
This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space $L(X)$ of an oriented differentiable stack $X$ and show…
We study actions of linear algebraic groups on finite-dimensional central simple algebras. We describe the fixed algebra for a broad class of such actions.
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differential Lie algebras of weight 1 when the action is the adjoint…
We introduce the notion of compatible actions in the context of split extensions of finite dimensional Lie algebras over a field. Using compatible actions, we construct a new resolution to compute the cohomology of semi-direct products of…
We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…
We study the modular class of $Q$-manifolds, and in particular of negatively graded Lie $\infty$-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that…
We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry…