Valerij N. Tolstoy | Searcharxiv

arXiv2015

Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincare / super-Euclidean r-matrices

We provide the classification of real forms of complex D=4 Euclidean algebra $\mathcalε(4; \mathbb{C}) = \mathfrak{o}(4;\mathbb{C})) \ltimes \mathbf{T}_{\mathbb{C}}^4$ as well as (pseudo)real forms of complex D=4 Euclidean superalgebras $\mathcalε(4|N; \mathbb{C})$ for N=1,2. Further we present our results: N=1 and N=2 supersymmetric D=4 Poincare and Euclidean r-matrices obtained by using D= 4 Poincare r-matrices provided by Zakrzewski [1]. For N=2 we shall consider the general superalgebras with two central charges.

hep-th↗

arXiv1993

Twisted Classical Poincaré Algebras

We consider the twisting of Hopf structure for classical enveloping algebra $U(\hat{g})$, where $\hat{g}$ is the inhomogenous rotations algebra, with explicite formulae given for $D=4$ Poincaré algebra $(\hat{g}={\cal P}_4).$ The comultiplications of twisted $U^F({\cal P}_4)$ are obtained by conjugating primitive classical coproducts by $F\in U(\hat{c})\otimes U(\hat{c}),$ where $\hat{c}$ denotes any Abelian subalgebra of ${\cal P}_4$, and the universal $R-$matrices for $U^F({\cal P}_4)$ are triangular. As an example we show that the quantum deformation of Poincaré algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincaré algebra. The interpretation of twisted Poincaré algebra as describing relativistic symmetries with clustered 2-particle states is proposed.

hep-th↗