Structure constant
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.
of an algebra 
over a field or over a commutative associative ring 
An element 
, 
, defined by the equality
 |
where 
is a fixed base of 
. The structure constants determine the algebra uniquely. If the 
are the structure constants of the algebra 
in another base 
, where 
, then
 |
Every identity that is true in 
can be expressed by relations between structure constants. For example,
 |
(commutativity);
 |
(associativity);
 |
(Jacobi's identity).
Comments
References
| [a1] | P.M. Cohn, "Algebra" , 2 , Wiley (1989) pp. 167ff |
How to Cite This Entry:
Structure constant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Structure_constant&oldid=12496
Structure constant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Structure_constant&oldid=12496
This article was adapted from an original article by L.A. Skornyakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article