Binary Lie algebra
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
-algebra
A linear algebra 
over a field 
any two elements of which generate a Lie subalgebra. The class of all binary Lie algebras over a given field 
generates a variety which, if the characteristic of 
is different from 2, is given by the system of identities
 | (*) |
where
 |
If the characteristic of 
is 2 and its cardinal number is not less than 4, the class of binary Lie algebras can be defined not only by the system of identities (*), but also by the identity
 |
The tangent algebra of an analytic local alternative loop is a binary Lie algebra and vice versa.
References
| [1] | A.I. Mal'tsev, "Analytic loops" Mat. Sb. , 36 (78) : 3 (1955) pp. 569–575 (In Russian) |
| [2] | A.T. Gainov, "Binary Lie algebras of characteristic two" Algebra and Logic , 8 : 5 (1969) pp. 287–297 Algebra i Logika , 8 : 5 (1969) pp. 505–522 |
How to Cite This Entry:
Binary Lie algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binary_Lie_algebra&oldid=18121
Binary Lie algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Binary_Lie_algebra&oldid=18121
This article was adapted from an original article by A.T. Gainov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article