Homotopy associative algebra

In mathematics, an algebra such as ( R , + , ⋅ ) {\displaystyle (\mathbb {R} ,+,\cdot )} has multiplication ⋅ {\displaystyle \cdot } whose associativity is well-defined on the nose. This means for any real numbers a , b , c ∈ R {\displaystyle a,b,c\in \mathbb {R} } we have a ⋅ ( b ⋅ c ) − ( a ⋅ b ) ⋅ c = 0 {\displaystyle a\cdot (b\cdot c)-(a\cdot b)\cdot c=0} .