# Structure constant

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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).