Related papers: Multiple Lie Derivatives and Forests
The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order…
The self-adjoint and $m$-sectorial extensions of coercive Sturm-Liouville operators are characterised, under minimal smoothness conditions on the coefficients of the differential expression.
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS) while at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows for use of…
We present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers Getzler's original functor but allows us to prove the…
In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and…
This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions that have shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle…
This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$, we describe a Lie algebroid structure on the direct sum vector bundle $P \times…
For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…
Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two…
We construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases…
The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front set satisfies some conditions. Thus, it is natural to investigate the topological properties of these operations between…
Motives of Brauer-Severi schemes of Cayley-smooth algebras associated to homogeneous superpotentials are used to compute inductively the motivic Donaldson-Thomas invariants of the corresponding Jacobian algebras. This approach can be used…
Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of…
We give an amalgamation construction of free multiple trees with a strongly transitive automorphism group. The construction shows that any partial codistance function on a tuple of finite trees can be extended to yield multiple trees.
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of…
Classical invariant theory establishes a systematic correspondence between algebraic and smooth invariants for compact and reductive Lie groups. However, the extension of these results to non-compact and non-reductive regimes remains a…
This paper derives rates of convergence of certain approximations of the Koopman operators that are associated with discrete, deterministic, continuous semiflows on a complete metric space $(X,d_X)$. Approximations are constructed in terms…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…