### Abstract

The construction of extended (N = 2 and N = 4) superconformal algebras (SCA) over very general classes of ternary algebras (triple systems) is given. For N = 2 this construction leads to superconformal algebras corresponding to certain Kählerian coset spaces of Lie groups with non-vanishing torsion. In general, a given Lie group admits more than one coset space of this type. The construction and a complete classification of N = 2 SCAs over Kantor triple system is given. In particular, the division algebras and their tensor products lead to N = 2 superconformal algebras associated with the coset spaces of the groups of the Magic Square. For a very special class of ternary algebras, namely the Freudenthal triple (FT) systems, the N = 2 superconformal algebras can be extended to N = 4 superconformal algebras with the gauge group SU(2)×SU(2)×U(1). The realization and a complete classification of N = 2 and N = 4.

Original language | English |
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Pages (from-to) | 688-712 |

Number of pages | 25 |

Journal | Nuclear Physics, Section B |

Volume | 373 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1992 Apr 13 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*373*(3), 688-712. https://doi.org/10.1016/0550-3213(92)90271-C