Abstract
The N=1 AdS-Lorentz superalgebra is studied and its relationship to semigroup expansion developed. Using this mathematical tool, the invariant tensors and Casimir operators are found. In terms of these invariants, a three-dimensional Chern–Simons supergravity action with AdS-Lorentz symmetry is constructed. The Killing spinors for a BTZ black-hole like solution of the theory are discussed.
Highlights
The application of S-expansion methods in the context of supergravity was first introduced in [15] and subsequently in [16] as an attempt to describe the low energy regime of M -Theory
We look for Casimir operators of degree two C = CABTATB, where CAB are given by the components of the symmetric invariant tensor TATB
In this work we have studied some aspects of the AdS-Lorentz superalgebra and the three-dimensional CS supergravity invariant under such symmetry
Summary
In Ref. [23] the semi-simple extension of the Poincare algebra iso(d − 1, 1), generated by Lorentz rotations {Jab} and translations {Pa}, has been carried out by the inclusion of a second-rank tensor generator {Zab}. [23] the semi-simple extension of the Poincare algebra iso(d − 1, 1), generated by Lorentz rotations {Jab} and translations {Pa}, has been carried out by the inclusion of a second-rank tensor generator {Zab}. This Lie algebra enhancement is isomorphic to the direct sum of the AdS and Lorentz algebra so(d − 1, 2) ⊕ so(d − 1, 1) in any dimension. We show that the (super)AdS-Lorentz algebra (2.1) can be derived as an application of the S-expansion procedure
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