We develop the theory of left-invariant generalized pseudo-Riemannian metrics on Lie groups. Such a metric accompanied by choice divergence operator gives rise to Ricci curvature tensor and we study corresponding Einstein equation. compute in terms tensors (on sum algebra its dual) encoding Courant algebroid structure, operator. The resulting expression is polynomial homogeneous degree two coef...

this paper aims to study a generalized double sinh-gordon equation, which appears in several physical phenomena such as integrable quantum field theory, kink dynamics and fluid dynamics. lie symmetry analysis together with the simplest equation method is used to obtain exact solutions for this equation. moreover, we derive conservation laws for the equation by using two different approaches, na...

The purpose of this paper is to give an algorithm for deciding the irreducibility of reduced algebroid curves over an algebraically closed field of arbitrary characteristic. To do this, we introduce a new notion of local tropical variety which is a straightforward extension of tropism introduced by Maurer, and then give irreducibility criterion for algebroid curves in terms local tropical varie...

This paper is the continuation of [12]. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the convolution of two coherent modules is the convolution of their Hochschild classes. We study with some details the case of symple...

Using the language of h-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, Fell GL n , from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra sln. We apply the generalized FRST construction and obtain an h-bialgebroid Fell M n . Natural analogs of the exterior algebra and ...

Abstract We define a new notion of fiberwise linear differential operator on the total space vector bundle E . Our main result is that operators are equivalent to (polynomial) derivations an appropriate line over E ? {E^{\ast}} believe this might represent first step towards definition m...