相关论文: Note on classical notion of Lee form

The generalized logarithmic electrodynamics with two parameters $\beta$ and $\gamma$ is considered. The indexes of refraction of light in the external magnetic field are calculated. In the case $\beta=\gamma$ we come to results obtained by…

This article is a survey about applications of bi-quantization theory in Lie theory. We focus on a conjecture of M. Duflo. Most of the applications are coming from our article with Alberto Cattaneo and some extensions are relating…

A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…

Variational and divergence symmetries are studied in this paper for linear equations of maximal symmetry in canonical form, and the associated first integrals are given in explicit form. All the main results obtained are formulated as…

We report on a detailed calculation of the anomaly coefficients for the odd and even parts of the $Z_2$-graded representation $\theta$ of the Lie algebra Lie$ G$ on the exterior algebra of dimension $2^n$ assuming that $G\subset U(n)$. The…

We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic…

Traditionally, Hodge structures are associated with complex projective varieties. In my expository lectures I discussed a non-commutative generalization of Hodge structures in deformation quantization and in derived algebraic geometry.

This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often…

The most natural first-order PDEs to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. In this work, we investigate the natural second-order conditions. We start at the linearised level, and construct the…

We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of It\^o calculus are an example, with four caveats: First, it says nothing about probability. Second,…

We compare a couple of notions of differential form on singular complex algebraic varieties, and relate them to the outermost associated graded spaces of the Hodge filtration of ordinary and intersection cohomology. In particular, we…

In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full…

This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…

We establish a closed formula for a singular vector of weight $\lambda-\beta$ in the Verma module of highest weight $\lambda$ for Lie superalgebra $\mathfrak{gl}(m|n)$ when $\lambda$ is atypical with respect to an odd positive root $\beta$.…

In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell…

We study solutions for the Hodge laplace equation $\Delta u=\omega $ on $p$ forms with $\displaystyle L^{r}$ estimates for $\displaystyle r>1.$ Our main hypothesis is that $\Delta $ has a spectral gap in $\displaystyle L^{2}.$ We use this…

We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvature flow self-shrinkers and expanders, translating…

We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. In particular, we exhibit an integral formula for the product of resurgent operators with algebraic singularities. This algebra…

In this note, we prove the regularity of eta forms by the Clifford asymptotics. Then we generalize this result to the equivariant case.

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…