Lie algebra

(redirected from Lie algebra homomorphism)

Lie algebra

[′lē ‚al·jə·brə]
(mathematics)
The algebra of vector fields on a manifold with additive operation given by pointwise sum and multiplication by the Lie bracket.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
That a Lie algebra homomorphism f between restricted Lie algebras is restricted if f ([x.sup.[p]]) = f [(x).sup.[p]] for all x in a generating set of the k-module L should be well known.
Denote by [Df.sub.*] (p) the induced Lie algebra homomorphism of the group homomorphism Df(p).
([a.sub.1], ..., [a.sub.q] [member of] [H.sub.1](X)), we obtain a graded Lie algebra homomorphism
It induces a Lie algebra homomorphism (denoted also by [rho]) from [GAMMA](E) to X(M), (iii) For any sections [s.sub.1],[s.sub.2] [member of] [member of] [GAMMA](E) and for any f [member of] F(M) the following identity holds