Algebra structure of conformal Killing-Yano forms in geometries with skew-symmetric torsion

ERTEM Ü., Kelekçi Ö., AÇIK Ö.

Classical and Quantum Gravity, vol.42, no.21, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 21
  • Publication Date: 2025
  • Doi Number: 10.1088/1361-6382/ae1097
  • Journal Name: Classical and Quantum Gravity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH
  • Keywords: generalized geometry, hidden symmetries, torsion
  • Ankara University Affiliated: Yes

Abstract

We consider conformal Killing-Yano (CKY) 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 CKY forms are found and a graded Lie bracket for CKY 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 CKY 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.