Related papers: Two-Dimensional Centrally Extended Quantum Galilei…
We investigate 2-dimensional Viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions…
This paper is an adaptation of a chapter from an upcoming monograph on noncommutative geometry and quantum groups. We present examples of non compact quantum groups which are deformations of low dimensional Lie groups. The paper is of…
Functional bases of second-order differential invariants of the Euclid, Poincar\'e, Galilei, conformal, and projective algebras are constructed. The results obtained allow us to describe new classes of nonlinear many-dimensional invariant…
We classify, up to isomorphism, twisted graded Calabi--Yau algebras of dimension two on two-vertex quivers. By work of Reyes and Rogalski, such algebras may be presented as quotients of translation quivers by mesh relations. We also…
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
I describe how integrable quantum field theories in 2 spacetime dimensions are characterized by infinite dimensional quantum group symmetries, namely the q-deformations of affine Lie algebras, and their Yangian limit. These symmetries can…
An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.
An explicit realization of the W(2,2) Lie algebra is presented using the famous bosonic and fermionic oscillators in physics, which is then used to construct the q-deformation of this Lie algebra. Furthermore, the quantum group structures…
There is a surge of research devoted to the formalism and physical manifestations of non-Lorentzian kinematical symmetries, which focuses especially on the ones associated with the Galilei and Carroll relativistic limits (the speed of light…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…
The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.
We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.
The cohomology and deformation theory of 3-Lie algebras are revisited. The theory of extending structures and unified product for 3-Lie algebras are developed.It is proved that the extending structures of 3-Lie algebras can be classified by…
The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some…