Lie Admissible Non-Associative Algebras

Abstract

A non-associative ring which contains a well-known associative ring or Lie ring is interesting. In this paper, a method to construct a Lie admissible non-associative ring is given; a class of simple non-associative algebras is obtained; all the derivations of the non-associative simple [Formula: see text] algebra defined in this paper are determined; and finally, a solid algebra is defined.