# Rigidity of Killing-Yano and conformal Killing-Yano superalgebras

## TL;DR

This paper demonstrates that Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds are rigid structures, with trivial second cohomology groups, indicating they are geometric invariants and cannot be deformed.

## Contribution

It establishes the rigidity of these superalgebras by proving their second cohomology groups are trivial, linking them to geometric invariants of constant curvature manifolds.

## Key findings

- Second cohomology groups are trivial
- Superalgebras cannot be deformed into others
- Superalgebras correspond to geometric invariants

## Abstract

Symmetry algebras of Killing vector fields and conformal Killing vectors fields can be extended to Killing-Yano and conformal Killing-Yano superalgebras in constant curvature manifolds. By defining $\mathbb{Z}$-gradations and filtrations of these superalgebras, we show that the second cohomology groups of them are trivial and they cannot be deformed to other Lie superalgebras. This shows the rigidity of Killing-Yano and conformal Killing-Yano superalgebras and reveals the fact that they correspond to geometric invariants of constant curvature manifolds. We discuss the structures and dimensions of these superalgebras on $AdS$ spacetimes as examples.