We discuss actions of Lie n-groups and the corresponding action Lie n-groupoids; discuss actions of Lie n-algebras (L∞-algebras) and the corresponding action Lie n-algebroids; and discuss the relation between the two by integration and differentiation. As an example of interest, we discuss the BRST complex that appears in quantum field theory. We describe it as the Chevalley-Eilenberg algebra o...

Supergroupoids, double structures, and equivariant cohomology by Rajan Amit Mehta Doctor of Philosophy in Mathematics University of California, Berkeley Professor Alan Weinstein, Chair Q-groupoids and Q-algebroids are, respectively, supergroupoids and superalgebroids that are equipped with compatible homological vector fields. These new objects are closely related to the double structures of Ma...

This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator K-theory). These dualities are expressed in terms of categories of modules. In this paper, we develop a general framework needed to describe these dualities. In various geometric contexts, e.g. complex geometry, gener...

We study Lie bialgebroid crossed modules which are pairs of algebroid in duality that canonically give rise to bialgebroids. A one-one correspondence between such and co-quadratic Manin triples [Formula: see text] is established, where a pair transverse Dirac structures text].

For a Lie groupoid G over smooth manifold M we construct the adjoint action of étale # germs local bisections on algebroid g . With this action, form associated convolution C c ∞ ( ) / R -bialgebra , We represent in algebra transversal distributions This construction extends Cartier-Gabriel decomposition Hopf with finite support group.

In this paper, we investigate families of singular holomorphic Lie algebroids on complex analytic spaces. We introduce and study a special type deformation called unfoldings algebroids, which generalizes the theory foliations developed by T. Suwa. show that one to correspondence between transversal flat connections natural algebroid bases exists.

In this paper, we construct a homotopy Poisson algebra of degree 3 associated to split Lie 2-algebroid, by which give new approach characterize 2-bialgebroid. We develop the differential calculus 2-algebroid and establish Manin triple theory for 2-algebroids. More precisely, notion strict Dirac structure define 2-algebroids be CLWX with two transversal structures. show that there is one-to-one ...

Let $n\ge 1$ and $A$ be a commutative algebra of the form $\boldsymbol k[x_1,x_2,\dots, x_n]/I$ where k$ is field characteristic $0$ $I\subseteq \boldsymbol x_n]$ an ideal. Assume that there Poisson bracket $\{\:,\:\}$ on $S$ such $\{I,S\}\subseteq I$ let us denote induced by as well. It well-known $[\mathrm d x_i,\mathrm x_j]:=\mathrm d\{x_i,x_j\}$ defines Lie $A$-module $\Omega_{A|\boldsymbol...

An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this to singular all 2-connected leaves and a wide class of 1-connected by proving Levi-Malcev theorem the semi-simple part holonomy Lie algebroid.