Abstract
In this paper, we classify filiform associative algebras of degree p over a field of characteristic zero. Moreover, over an algebraically closed field of characteristic zero, we also classify filiform nilpotent associative algebras and naturally graded quasi-filiform nilpotent associative algebras, described through the characteristic sequence \(C({\mathcal {A}})=(n-2,1,1)\) or \(C({\mathcal {A}})=(n-2,2)\).
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This work was supported by Agencia Estatal de Investigación (Spain), Grant MTM2016-79661-P and by Xunta de Galicia, Grant ED431C 2019/10 (European FEDER support included, UE).
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Karimjanov, I.A., Ladra, M. Some Classes of Nilpotent Associative Algebras. Mediterr. J. Math. 17, 70 (2020). https://doi.org/10.1007/s00009-020-1504-x
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DOI: https://doi.org/10.1007/s00009-020-1504-x
Keywords
- Associative algebras
- nilpotent
- null-filiform
- naturally graded
- filiform
- quasi-filiform
- characteristic sequence
- left multiplication operator