Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion
arXiv:2508.05117 · doi:10.1088/1361-6382/ae1097
Abstract
We consider conformal Killing-Yano forms corresponding to the antisymmetric generalizations of conformal Killing vectors to higher degree forms in the presence of skew-symmetric torsion. Integrability conditions for torsionful conformal Killing-Yano forms are found and a graded Lie bracket for conformal Killing-Yano forms to constitute a graded Lie algebra structure is proposed. It is found that a graded Lie algebra structure for a special subset of torsionful conformal Killing-Yano forms can be constructed for a closed and parallel skew-symmetric torsion on constant curvature and Einstein manifolds. Similar structure for generalized hidden symmetries defined from generalized connection in generalized geometry is also constructed.
arXiv comment12 pages, published version
References in corpus (20)
- Supergravity as Generalised Geometry I: Type II Theories
- Supersymmetric AdS_5 Solutions of Type IIB Supergravity
- Killing-Yano Tensors, Rank-2 Killing Tensors, and Conserved Quantities in Higher Dimensions
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Dirac symmetry operators from conformal Killing-Yano tensors
- Generalized Killing-Yano equations in D=5 gauged supergravity
- Conserved gravitational charges from Yano tensors
- Dirac Equation in Kerr-NUT-(A)dS Spacetimes: Intrinsic Characterization of Separability in All Dimensions
- Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
- Symmetries of the Dirac operator with skew-symmetric torsion
- AdS_3 x S^3 x S^3 x S^1 Solutions of Type IIB String Theory
- First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition
- Do Killing-Yano tensors form a Lie Algebra?
- Basic Gravitational Currents and Killing-Yano Forms
- Lie algebra of conformal Killing-Yano forms
- Twistor spinors and extended conformal superalgebras
- Symmetry operators of Killing spinors and superalgebras in AdS_5
- Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
- Couplings of gravitational currents with Chern-Simons gravities
- Generalized symmetry superalgebras