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- Title
THE EQUATION [x,u] + [y,v] = 0 IN FREE LIE ALGEBRAS.
- Authors
REMESLENNIKOV, VLADIMIR; STÖHR, RALPH; Plotkin, E.
- 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 [x1,x2] + [x3,x4] = 0.
- Subjects
LIE algebras; FREE algebras; HOMOGENEOUS spaces; LINEAR algebra; MATHEMATICAL analysis; MATHEMATICAL series
- Publication
International Journal of Algebra & Computation, 2007, Vol 17, Issue 5/6, p1165
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196707004104