## 2006.106: THE EQUATION [x,u]+[y,v]=0 IN FREE LIE ALGEBRAS

2006.106:
Vladimir Remeslennikov and Ralph Stöhr
(2007)
*THE EQUATION [x,u]+[y,v]=0 IN FREE LIE ALGEBRAS.*
Internat. J. Algebra Comput., 17 (no. 5/6).
pp. 1165-1187.
ISSN 1749-9097

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## Abstract

We investigate equations of the form [x,u]+[y,v]=0 over a free Lie algebra L. In the case where u and v are free generators of L, we exhibit two series of solutions, we work out the dimensions of the homogeneous components of the solution space, and we determine its radical. In the general case we show that the results on free generator coefficients are sufficient to obtain the solution space up to finite codimension. As an application we determine the radical of the bilinear equation [x_1,x_2]+[x_3,x_4]=0.

Item Type: | Article |
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Uncontrolled Keywords: | Equations, Free Lie Algebras |

Subjects: | MSC 2000 > 17 Nonassociative rings and algebras |

MIMS number: | 2006.106 |

Deposited By: | Prof Ralph Stöhr |

Deposited On: | 13 December 2007 |

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