Related papers: Semidirect products of representations up to homot…
Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential…
We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…
We study integrable systems on the semidirect product of a Lie group and its Lie algebra as the representation space of the adjoint action. Regarding the tangent bundle of a Lie group as phase space endowed with this semidirect product Lie…
This paper studies differential graded modules and representations up to homotopy of Lie $n$-algebroids, for general $n\in\mathbb{N}$. The adjoint and coadjoint modules are described, and the corresponding split versions of the adjoint and…
We study and classify the 3-dimensional Hom-Lie algebras over $\mathbb{C}$. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space…
In this work we solve the problem of providing a Morita invariant definition of Lie and Courant algebroids over Lie groupoids. By relying on supergeometry, we view these structures as instances of vector fields on graded groupoids which are…
This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…
We show Lie algebra versions of some results on homological finiteness properties of subdirect products of groups, including a version of the 1-2-3 Theorem.
In this paper, we introduce the notion of generalized representation of a $3$-Lie algebra, by which we obtain a generalized semidirect product $3$-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of…
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidirect products and describe the structure of their prime…
We construct loops which are semidirect products of groups of affinities. As their elements in many cases one may take transversal subspaces of an affine space. In particular we obtain in this manner smooth loops having Lie groups of affine…
We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of…
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…
Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB -algebroid. There is a close relation between two term…
Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category…
The propose of this paper is to extend generalized representations of 3-Lie algebras to Hom-type algebras. We introduce the concept of generalized representation of multiplicative 3-Hom-Lie algebras, develop the corresponding cohomology…
We study the general geometrical structure of the coadjoint orbits of a semidirect product formed by a Lie group and a representation of this group on a vector space. The use of symplectic induction methods gives new insight into the…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation…
We exhibit in this article a contraction of the direct product Lie algebra $g\oplus g$ of a finite-dimensional complex Lie algebra $g$ onto the semi-direct product Lie algebra $g\rtimes g$, where the first factor $g$ is viewed as a trivial…