# Structure constant

From Encyclopedia of Mathematics

*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://www.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