Algebra, Algebra, You Were So Tough

Twisted Conformal Algebra so(4,2)

A new twisted deformation, Uz(so(4, 2)), of the conformal algebra of the (3+1)-dimensional Minkowskian spacetime is presented. This construction is provided by a classical r-matrix spanned by ten Weyl–Poincaré generators, which generalizes non-standard quantum deformations previously obtained for so(2, 2) and so(3, 2). However, by introducing a conformal nullplane basis it is found that the twi...

Lie triple derivation algebra of Virasoro-like algebra

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

A new quantum so(2,2) algebra

By starting from the non-standard quantum deformation of the sl(2,R) algebra, a new quantum deformation for the real Lie algebra so(2, 2) is constructed by imposing the former to be a Hopf subalgebra of the latter. The quantum so(2, 2) algebra so obtained is realized as a quantum conformal algebra of the (1 + 1) Minkowskian spacetime. This Hopf algebra is shown to be the symmetry algebra of a t...

On dimensions of derived algebra and central factor of a Lie algebra

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

N=2 Superconformal Symmetry and SO(2,l) Current Algebra