Realizations of Galilei algebras

`-conformal Galilei algebras

Inequivalent N = 2 supersymmetrizations of the `-conformal Galilei algebra in d-spatial dimensions are constructed from the chiral (2, 2) and the real (1, 2, 1) basic supermultiplets of the N = 2 supersymmetry. For non-negative integer and half-integer ` both superalgebras admit a consistent truncation with a (different) finite number of generators. The real N = 2 case coincides with the supera...

Realizations of real semisimple low-dimensional Lie algebras Realizations of real semisimple low-dimensional Lie algebras

A complete set of inequivalent realizations of threeand four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained. Representations of Lie algebras by vector fields are widely applicable e.g. in integrating of ordinary differential equations, group classification of partial differential equations, the theory of differential...

Kinematical expansions: from Galilei to de Sitter algebras

Expansions of Lie algebras are the opposite process of contractions. Starting from a Lie algebra, the expansion process goes to another one, nonisomorphic and less abelian. We propose an expansion method based in the Casimir invariants of the initial and expanded algebras and where the free parameters involved in the expansion are the curvatures of their associated homogeneous spaces. This meth...

Explicit field realizations of W algebras

The fact that certain non-linear W2,s algebras can be linearized by the inclusion of a spin-1 current can provides a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar fields and spinor fields respectively. Then, after a basis inverting, the realizations of W2,s algebras ...

Loop realizations of quantum affine algebras