Commutant-associative algebra

Commutant-associative algebra

In abstract algebra, a commutant-associative algebra is a nonassociative algebra over a field whose multiplication satisfies the following axiom:

([A1,A2],[A3,A4],[A5,A6]) = 0,

where [AB] = AB − BA is the commutator of A and B and (ABC) = (AB)C – A(BC) is the associator of A, B and C.

In other words, an algebra M is commutant-associative if the commutant, i.e. the subalgebra of M generated by all commutators [AB], is an associative algebra.

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References


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