Related papers: Poincare Algebra Extension with Tensor Generator
We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification of diffeomorphism cocycles. We also…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
We consider general linear superalgebra (type A) and tensor with Laurent polynomial ring in several variables. We then consider the universal central extension of this Lie superalgebra which we call toroidal superalgebra. We give a faithful…
The Poincare mass operator can be represented in terms of a Cl(3,0) Clifford algebra. With this representation the quadratic Dirac equation and the Maxwell equations can be derived from the same mathematical structure.
Here we consider a gravitational action having local Poincare invariance which is given by the dimensional continuation of the Euler density in ten dimensions. It is shown that the local supersymmetric extension of this action requires the…
In this paper we briefly review the main results obtained in arXiv:0812.1982, where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincare' algebra in 4…
Casimir operators -- the generators of the center of the enveloping algebra -- are described for simple or close to them ``classical'' finite dimensional Lie superalgebras with nondegenerate symmetric even bilinear form in Sergeev A., The…
A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A…
We construct Wigner's continuous spin representations of the Poincar\'e algebra for massless particles in higher dimensions. The states are labeled both by the length of a space-like translation vector and the Dynkin indices of the {\it…
It is known that every irreducible unitary representation of positive energy of the Poincar\'e group can be realized as a subspace of tensor fields on Minkowski spacetime subjected to suitable partial differential equations. We first…
We classify all massive irreducible representations of super Poincar\'e in D=10. New Casimir operators of super Poincar\'e are presented whose eigenvalues completely specify the representation. It is shown that a scalar superfield contains…
Super Poincare algebra in D = 6 space-time dimensions has been analysed in terms of quaternion analyticity of Lorentz group. Starting the connection of quaternion Lorentz group with SO(1; 5) group, the SL(2;H) spinors for Dirac & Weyl…
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
In the present paper we construct deformations of the Poincar\'e algebra as representations on a noncommutative spacetime with canonical commutation relations. These deformations are obtained by solving a set of conditions by an appropriate…
Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
We construct the parabosonic string formalism based on the paraquantization of both the center of mass variables and the excitation modes of the string. A critical study of the different commutators of the Poincar\'{e} algebra based on the…
We introduce the notion of \pi-extension of the semigroup \mathbb{Z}_+ and study the extensions of the Toeplitz algebras by isometric operators. We show that when the action of the Toeplitz algebra is irreducible all such extensions…
The notion of Poincare gauge manifold ($G$), proposed in the context of an (1+1) gravitational theory by Cangemi and Jackiw (D. Cangemi and R. Jackiw, Ann. Phys. (N.Y.) 225 (1993) 229), is explored from a geometrical point of view. First…
We describe the set of generalized Poincare and conformal superalgebras in D=4,5 and 7 dimensions as two sequences of superalgebraic structures, taking values in the division algebras R, C and H. The generalized conformal superalgebras are…