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.
|Number of pages||9|
|Journal||Journal of Mathematical Sciences|
|Publication status||Published - 2005 Dec 1|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics