Generalized symmetry superalgebras

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AÇIK Ö., Ertem U.

JOURNAL OF MATHEMATICAL PHYSICS, vol.62, no.5, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1063/5.0033936
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, INSPEC, MathSciNet, zbMATH, DIALNET
  • Ankara University Affiliated: Yes

Abstract

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano forms and special conformal Killing-Yano forms. After defining the Lie algebra structure of hidden symmetries generated by Killing spinors, we construct symmetry operators as the generalizations of the Lie derivative on spinor fields. All these constructions together constitute the structure of generalized symmetry superalgebras. We exemplify the construction on weak G(2) and nearly Kahler manifolds.