On the Multiplier of Filiform Filippov Algebras

Suppose A is a finite dimensional filiform Filippov algebra. Given the dimension of Schur multiplier of filiform Filippov algebras A ( $$\dim \mathcal {M}(A)$$ ), one associates a non-negative integer t(A) to such an A. In the first part of this paper, we classify all filiform Filippov alegbras A for $$0\leqslant t(A)\leqslant 23$$ . Also, it is known that the dimension of Schur multiplier of the filiform Filippov algebra A is bounded by $$\dim A^2(n-1)$$ . In the second part of this paper, we give the structure of all filiform Filippov algebras A when $$\dim \mathcal {M}(A)=\dim A^2(n-1)$$ . Finally, we show that all of these filiform Filippov algebras are capable.