Abstract
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.
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Darabi, H., Eshrati, M. & Jabbar Nezhad, B. On the Multiplier of Filiform Filippov Algebras. Results Math 76, 190 (2021). https://doi.org/10.1007/s00025-021-01498-z
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DOI: https://doi.org/10.1007/s00025-021-01498-z