Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Lean, Madeleine Jotz"'
The core diagram of a double Lie algebroid consists in the core of the double Lie algebroid, together with the two core-anchor maps to the sides of the double Lie algebroid. If these two core anchors are surjective, then the double Lie algebroid and
Externí odkaz:
http://arxiv.org/abs/2103.13189
Autor:
Heuer, Malte, Lean, Madeleine Jotz
This paper studies linear generalised complex structures over vector bundles, as a generalised geometry version of holomorphic vector bundles. In an adapted linear splitting, a linear generalised complex structure on a vector bundle $E\to M$ is equiv
Externí odkaz:
http://arxiv.org/abs/2011.14652
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 coadjoint
Externí odkaz:
http://arxiv.org/abs/2001.01101
Autor:
Lean, Madeleine Jotz
This short note gives a geometric interpretation of the Atiyah class of a Lie pair. It proves that it vanishes if the subalgebroid is the kernel of a fibration of Lie algebroids. In other words, the Atiyah class of a Lie pair vanishes if the subalgeb
Externí odkaz:
http://arxiv.org/abs/1910.04492
Autor:
Lean, Madeleine Jotz
This paper considers the Pontryagin characters of graded vector bundles of finite rank, in the cohomology vector spaces of a Lie algebroid over the same base. These Pontryagin characters vanish if the graded vector bundle carries a representation up
Externí odkaz:
http://arxiv.org/abs/1905.10237
Autor:
Lean, Madeleine Jotz
This paper provides an alternative, much simpler, definition for Li-Bland's LA-Courant algebroids, or Poisson Lie 2-algebroids, in terms of split Lie 2-algebroids and self-dual 2-representations. This definition generalises in a precise sense the cha
Externí odkaz:
http://arxiv.org/abs/1811.04842
Autor:
Heuer, Malte, Lean, Madeleine Jotz
This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove that any $n$-
Externí odkaz:
http://arxiv.org/abs/1809.01484
Autor:
Lean, Madeleine Jotz
Publikováno v:
Pacific J. Math. 301 (2019) 143-188
Li-Bland's correspondence between linear Courant algebroids and Lie $2$-algebroids is explained and shown to be an equivalence of categories. Decomposed VB-Courant algebroids are shown to be equivalent to split Lie 2-algebroids in the same manner as
Externí odkaz:
http://arxiv.org/abs/1712.07035
Autor:
Lean, Madeleine Jotz
This paper describes an equivalence of the canonical category of $\mathbb N$-manifolds of degree $2$ with a category of involutive double vector bundles. More precisely, we show how involutive double vector bundles are in duality with double vector b
Externí odkaz:
http://arxiv.org/abs/1707.06798
In this note we prove that, for a vector bundle $E$ over a manifold $M$, a Dorfman bracket on $TM\oplus E^*$ anchored by $\operatorname{pr}_{TM}$ and with $E$ a vector bundle over $M$, is equivalent to a lift from $\Gamma(TM\oplus E^*)$ to linear sec
Externí odkaz:
http://arxiv.org/abs/1610.05986