In this paper, the Boiti–Leon–Pempinelli system in (2+1)-dimensions is revisited for Lie symmetries and invariant solutions. An infinite dimensional algebra obtained using invariance criterion further classified into one, two three-dimensional optimal list of subalgebras. We obtain new explicit exact solutions involving arbitrary functions that have been missed previous work (Kumar et al. Compu...

This paper studies the canonical symmetric connection $\nabla$ associated to any Lie group $G$. The salient properties of are stated and proved. symmetries geodesic system a general linear formulated. results then applied in special case where algebra $\g$ $G$, has codimension one abelian nilradical. conditions that determine symmetry such completely integrated. Finally obtained compared with s...

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of ...

BMS group (and it's various generalizations) at null infinity have been studied extensively in the literature as symmetry of asymptotically flat spacetimes. The intricate relationship between soft theorems and symmetries also motivated definition such asymptotic to time-like infinity. Although vector fields that generate (generalized) algebra was defined literature, has not investigated. In thi...

The infinite dimensional geometry of the qR–conformal symmetries (the hidden symmetries in the Verma modules over sl(2,C) generated by the spin 2 tensor operators) is discussed. This paper opens the series of articles supplemental to [1], which also lie in lines of the general ideology exposed in the review [2]. The main purpose of further activity, which has its origin and motivation presumabl...

in this paper, we classify the indecomposable non-nilpotent solvable lie algebras with $n(r_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $n(r_n,m,r)$.we also prove that these solvable lie algebras are complete and unique, up to isomorphism.

Many of important properties of integrable systems and conformal models in two dimensions originate from underlying infinite-dimensional symmetries. Higher-spin (HS) extensions of the Virasoro symmetry acquired much attention during recent years. In particular, d2 conformal matter models with gauged HS symmetries have been extensively studied for the cases of WN [1], ω∞ [2] and W1+∞ [3, 4] alge...

This is an entirely expository piece: the main results discussed are very wellknown and the approach we take is not really new, although the presentation may be somewhat different to what is in the literature. The author’s main motivation for writing this piece comes from a feeling that the ideas deserve to be more widely known. Let g be a Lie algebra over R or C. . A vector subspace I ⊂ g is a...

Let M0 = G0/H be a (pseudo)-Riemannian homogeneous spin manifold, with reductive decomposition g0 = h + m and let S(M0) be the spin bundle defined by the spin representation Ãd : H → GLR(S) of the stabilizer H . This article studies the superizations of M0, i.e. its extensions to a homogeneous supermanifold M = G/H whose sheaf of superfunctions is isomorphic to Λ(S(M0)). Here G is the Lie super...

‎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...