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

Abstract

We provide the classification of real forms of complex D=4 Euclidean algebra $\epsilon (4;\mathbb{C})=\mathfrak{o}(4;\mathbb{C}))⋉{\mathbf{T}}_{\mathbb{C}}^4$ as well as (pseudo)real forms of complex D=4 Euclidean superalgebras $\epsilon (4|N;\mathbb{C})$ 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.

20 pages, presented at XXIII-th International Conference on Integrable Systems and Quantum Symmetries, Prague, June 2015; to be published in JPhysA Conference Series, ed. C. Burdik, S.Posta and O.Navratil

References in corpus (3)

• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• Rigid 4D N=2 supersymmetric backgrounds and actions

Cited by in corpus (4)

• Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries