Zobrazeno 1 - 10
of 80
pro vyhledávání: '"P. Stienon"'
Given an inclusion $A\to L$ of Lie algebroids sharing the same base manifold $M$, i.e. a Lie pair, we prove that the space $\Gamma(\Lambda^\bullet A^\vee)\otimes_{C^\infty(M)} \frac{U(L)}{U(L)\cdot\Gamma(A)}$ admits a natural $A_\infty$ algebra struc
Externí odkaz:
http://arxiv.org/abs/2210.16769
This paper is devoted to the study of the relation between `formal exponential maps,' the Atiyah class, and Kapranov $L_\infty[1]$ algebras associated with dg manifolds in the $C^\infty$ context. Given a dg manifold, we prove that a `formal exponenti
Externí odkaz:
http://arxiv.org/abs/2106.00812
Publikováno v:
J. Noncommut. Geom. 15.2 (2021), pp. 643-711
We prove that the spaces $\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee \otimes_R\mathcal{T}_{\operatorname{poly}}^{\bullet}\big)$ and $\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee)\otimes_R\mathcal{D}_{\operatorname{poly}}^{\bullet}\b
Externí odkaz:
http://arxiv.org/abs/1901.04602
Publikováno v:
Comm. Math. Phys. 375.3 (2020), pp. 1717-1760
We study the shifted analogue of the "Lie--Poisson" construction for $L_\infty$ algebroids and we prove that any $L_\infty$ algebroid naturally gives rise to shifted derived Poisson manifolds. We also investigate derived Poisson structures from a pur
Externí odkaz:
http://arxiv.org/abs/1712.00665
Publikováno v:
C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 582-589
To any $\mathfrak{g}$-manifold $M$ are associated two dglas $\operatorname{tot}\big(\Lambda^{\bullet} \mathfrak{g}^\vee \otimes_{\Bbbk} T_{\operatorname{poly}}^{\bullet} \big)$ and $\operatorname{tot} \big(\Lambda^{\bullet} \mathfrak{g}^\vee\otimes_{
Externí odkaz:
http://arxiv.org/abs/1701.04872
Publikováno v:
Adv. Math. 352 (2019), 406-482
$\newcommand{\poly}{_{\operatorname{poly}}^{\bullet}}\newcommand{\td}{(\operatorname{td}_{L/A}^{\nabla})^{\frac{1}{2}}}\newcommand{\cx}[1]{\operatorname{tot}\big(\Gamma(\Lambda^\bullet A^\vee)\otimes_R\mathcal{#1}\poly\big)}\newcommand{\cy}[1]{\mathb
Externí odkaz:
http://arxiv.org/abs/1605.09722
Autor:
Stiénon, Mathieu, Xu, Ping
Publikováno v:
Math. Ann. 378.1-2 (2020), pp. 729-762
Given any pair $(L,A)$ of Lie algebroids, we construct a differential graded manifold $(L[1]\oplus L/A,Q)$, which we call Fedosov dg manifold. We prove that the cohomological vector field $Q$ constructed on $L[1]\oplus L/A$ by the Fedosov iteration m
Externí odkaz:
http://arxiv.org/abs/1605.09656
Autor:
Liao, Hsuan-Yi, Stiénon, Mathieu
Publikováno v:
Int. Math. Res. Not. IMRN 2019, no. 3, 700-730
We introduce, for every $\mathbb{Z}$-graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new construction of a Fedosov type resolution of the algebra of smooth func
Externí odkaz:
http://arxiv.org/abs/1508.02780
Publikováno v:
Comptes Rendus Mathematique 353 (2015), no. 4, 357-362
We introduce the notions of Atiyah class and Todd class of a differential graded vector bundle with respect to a differential graded Lie algebroid. We prove that the space of vector fields on a dg-manifold with homological vector field $Q$ admits a s
Externí odkaz:
http://arxiv.org/abs/1502.03119
Publikováno v:
C. R. Math. Acad. Sci. Paris 352 (2014), no. 11, 929-933
The quotient $L/A[-1]$ of a pair $A\hookrightarrow L$ of Lie algebroids is a Lie algebra object in the derived category $D^b(\mathscr{A})$ of the category $\mathscr{A}$ of left $\mathcal{U}(A)$-modules, the Atiyah class $\alpha_{L/A}$ being its Lie b
Externí odkaz:
http://arxiv.org/abs/1409.6803