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All Lie bialgebra structures for the (1+ 1)-dimensional centrally extended Schrödinger algebra are explicitly derived and proved to be of the coboundary type. Therefore, since all of them come from a classical r-matrix, the complete family of Schrödinger Poisson–Lie groups can be deduced by means of the Sklyanin bracket. All possible embeddings of the harmonic oscillator, extended Galilei and g...

Spinor representation of the group GL(4,R) is needed for correct description of the Fermi fields on Riemann space, such as the space-time of general relativity. It is used for two purposes: to define the connectivity and covariant derivative of spinor field and to define the Lie derivative. Recent publications [1–3] have reminded of this problem. The important problem for definition of Fermi fi...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

In this work, a complete classification of the Lie group symmetries for generalization Chazy equation was carried out and equivalence generalized is calculated used to present principal algebra equation.

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‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...