Related papers: Kinematical Lie algebras in 2+1 dimensions
For most complex 9-dimensional filiform Lie algebra we find another non isomorphic Lie algebra that degenerates to it. Since this is already known for nilpotent Lie algebras of rank $\geq 1$, only the characteristically nilpotent ones…
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
This work presents a classical Lie point symmetry analysis of a two-component, non-isospectral Lax pair of a hierarchy of partial differential equations in $2+1$ dimensions, which can be considered as a modified version of the Camassa-Holm…
A Lie algebra structure on variation vector fields along an immersed curve in a $2$-dimensional real space form is investigated. This Lie algebra particularized to plane curves is the cornerstone in order to define a Hamiltonian structure…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the…
In this paper, the possible values of commutativity degree of Lie algebras are determined. Also, we define the asymptotic commutativity degree of Lie algebras and obtain the asymptotic commutativity degree for some of them. Moreover, we…
We introduce a new construction of bilinear invariant forms on Lie algebras, based on the method of graded contractions. The general method is described and the $\Bbb Z_2$-, $\Bbb Z_3$-, and $\Bbb Z_2\otimes\Bbb Z_2$-contractions are found.…
All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them…
Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…
We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.
All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.
We prove explit formulas for the decomposition of a differential graded Lie algebra into a minimal and a linear $L_\infty$-algebra. We define a category of metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the…
We classify all 2-term $L_\infty$-algebras up to isomorphism. We show that such $L_\infty$-algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie…
Denote m_0 the infinite dimensional N-graded Lie algebra defined by basis e_i, i>= 1 and relations [e_1,e_i] = e_(i+1) for all i>=2. We compute in this article the bracket structure on H1(m_0,m_0), H2(m_0,m_0) and in relation to this, we…
Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…
We define the notion of a Lie superalgebra over a field $k$ of characteristic $2$ which unifies the two pre-existing ones - $\mathbb{Z}/2$-graded Lie algebras with a squaring map and Lie algebras in the Verlinde category ${\rm Ver}_4^+(k)$,…
A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…
In this paper, the Boiti Leon Pempinelli system in (2+1)-dimensions is revisited for Lie symmetries and invariant solutions. An infinite-dimensional Lie algebra is obtained using the Lie invariance criterion and is further classified into…