Construction of examples of Lie-admissible algebras

In this discussion we examine general methods of constructing Lie-admissible algebras. Many of the techniques which we survey have been known since the inception of Lie-admissible studies, many have developed as the subject has evolved especially in the last five years, and many are appearing for the first time in this article. In presenting these examples we have taken two different approaches. First we have looked for common themes to unite the seemingly disparate array of algebras in the literature. In this regard we discuss six general classes of Lie-admissible algebras: (1) algebras arising by adjoining a symmetric multiplication to a Lie algebra product; (2) deformations and cohomology extensions of Lie, associative and Lie-admissible algebras; (3) mutation algebras; (4) nodal algebras; (5) Lie superalgebras; and (6) algebras resulting from structure theorems. Our second approach is to single out particular algebras within our general classes to illustrate with special cases how some concrete calculations might proceed. The special cases studied have been chosen because of their potential physical relevance.