### Abstract

The theory of functional identities is applied to the classification of the third-power-associative products * which can be defined on certain Lie subalgebras A of the matrix algebra M _{n} (F) over a field F such that x*y - y*x = xy - yx for all x, y A, where xy denotes the usual associative product in M _{n} (F) and A is the matrix algebra itself, a Lie ideal, a one-sided ideal, the Lie algebra of skew elements, or the algebra of upper triangular matrices.

Original language | English |
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Pages (from-to) | 5939-5947 |

Number of pages | 9 |

Journal | Journal of Mathematical Sciences |

Volume | 131 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2005 Dec 1 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Applied Mathematics

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## Cite this

Beidar, K. I., Chebotar, M. A., Fong, Y., & Ke, W-F. (2005). On certain power-associative, Lie-admissible subalgebras of matrix algebras.

*Journal of Mathematical Sciences*,*131*(5), 5939-5947. https://doi.org/10.1007/s10958-005-0452-0