Related papers: DGLA Dg and BV formalism

We equip Ellis and Brundan's version of the odd categorified quantum group for sl(2) with a differential giving it the structure of a graded dg-2-supercategory. The presence of the super grading gives rise to two possible…

We give explicit formulae for differential graded Lie algebra (DGLA) models of 3-cells. In particular, for a cube and an $n$-faceted banana-shaped 3-cell with two vertices, $n$ edges each joining those two vertices and $n$ bi-gon 2-cells,…

In this paper we study modular $G$-equivariant fusion categories and their extended Verlinde algebras. We dicuss settings in which fusion rules are diagonalizable. In particular, when $G = \mathbb{Z}_{2}$ we generalize the Verlinde formula.…

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…

The space D(k,p) of differential operators of order at most k, from the differential forms of degree p of a smooth manifold M into the functions of M, is a module over the Lie algebra of vector fields of M, when it's equipped with the…

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…

We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…

In BV formalism we can consider a Lagrangian submanifold as a gauge condition. Starting with the BV action functional we construct a closed form on the space of Lagrangian submanifolds. If the action functional is invariant with respect to…

Let G be a complex semisimple group and U its maximal unipotent subgroup. We study the algebra D(G/U) of algebraic differential operators on G/U and also its quasi-classical counterpart: the algebra of regular functions on the cotangent…

Preprint HAL-00507788 (2010) from the CNRS open online arxive HAL. The equivariantly closed matrix integrals introduced in [B06], are studied in the case of the graded associative algebras with odd or even scalar product.I prove that the…

The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…

We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum physics. A general operator formalism is given to solve spectral problems using…

We define the braided differential algebras which can be interpreted as quantization of the differential operator algebra defined on some algebraic varieties supplied with the action of the group GL(m). The algebra is generated by right…

The joint spectral theory of a system of pairwise commuting self-adjoint left-invariant differential operators L_1,...,L_n on a connected Lie group G is studied, under the hypothesis that the algebra generated by them contains a "weighted…

For a real or complex semisimple Lie group $G$ and two nested parabolic subgroups $Q\subset P\subset G$, we study parabolic geometries of type $(G,Q)$. Associated to the group $P$, we introduce a class of relative natural bundles and…

This paper studies properties of the logic BV, which is an extension of multiplicative linear logic (MLL) with a self-dual non-commutative operator. BV is presented in the calculus of structures, a proof theoretic formalism that supports…

Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras…

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such…

Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a…

Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…