Free Lie Algebra

In mathematics, a free Lie algebra, over a given field K, is a Lie algebra generated by a set X, without any imposed relations.

Read more about Free Lie Algebra:  Definition, Universal Enveloping Algebra, Hall Sets, Lyndon Basis, Shirshov–Witt Theorem, Applications

Famous quotes containing the words free, lie and/or algebra:

    “If I had not come to America, where I felt free to formulate tentatively insights at which I had empathically arrived, I would have accomplished very little. I would never have begun to publish, to teach, to undertake research. Because if one does not find an assenting echo to one’s ideas, if one is passed over, as I was in Vienna, then one cannot create. To create, after all, is to believe that what one says will count.”
    —Margaret S. Mahler (1897–1985)

    “The point is children lie to others for good and sufficient reasons, but they don’t kid themselves. They know who did what, but they feel no moral imperative to inform grownups.”
    —Leontine Young (20th century)

    “Poetry has become the higher algebra of metaphors.”
    —José Ortega Y Gasset (1883–1955)