Abstract
In this paper, we classify naturally graded complex quasi-filiform nilpotent associative algebras described using the characteristic sequence \(C(\mathcal {A})= (n-2,1,1)\) or \(C(\mathcal {A})=(n-2,2)\).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ancochea Bermúdez, J.M., Campoamor-Stursberg, R., GarcÃa Vergnolle, L.: Classification of Lie algebras with naturally graded quasi-filiform nilradicals. J. Geom. Phys. 61(11), 2168–2186 (2011)
Ayupov, S.A., Omirov, B.A.: On some classes of nilpotent Leibniz algebras. Siberian Math. J. 42(1), 15–24 (2001)
Camacho, L.M., Gómez, J.R., Gónzalez, A.J., Omirov, B.A.: Naturally graded quasi-filiform Leibniz algebras. J. Symb. Comput. 44(5), 527–539 (2009)
Camacho, L.M., Gómez, J.R., González, A.J., Omirov, B.A.: Naturally graded 2-filiform Leibniz algebras. Commun. Algebra 38(10), 3671–3685 (2010)
GarcÃa Vergnolle, L., Remm, E.: Complex structures on quasi-filiform Lie algebras. J. Lie Theory 19(2), 251–265 (2009)
Gómez, J.R., Jiménez-Merchán, A.: Naturally graded quasi-filiform Lie algebras. J. Algebra 256(1), 211–228 (2002)
Karimjanov, I.A., Ladra, M.: Some classes of nilpotent associative algebras. Mediterr. J. Math. (to appear). https://doi.org/10.1007/s00009-020-1504-x
Masutova, K.K., Omirov, B.A.: On some zero-filiform algebras. Ukrainian Math. J. 66(4), 541–552 (2014)
Vergne, M.: Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes. Bull. Soc. Math. France 98, 81–116 (1970)
Acknowledgements
We thank the referees for the helpful comments and suggestions that contributed to improving this paper.
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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Karimjanov, I.A., Ladra, M. (2020). Naturally Graded Quasi-Filiform Associative Algebras. In: Ortegón Gallego, F., GarcÃa GarcÃa, J. (eds) Recent Advances in Pure and Applied Mathematics. RSME Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-41321-7_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-41321-7_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-41320-0
Online ISBN: 978-3-030-41321-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)