Abstract
We describe the (n + s)-dimensional solvable Leibniz algebras whose nilradical has characteristic sequence (m1, …, ms), where m1 +⋯+ ms = n. The completeness and cohomological rigidity of this algebra are proved.
Similar content being viewed by others
References
Blokh A., “On a generalization of the concept of Lie algebras,” Dokl. Akad. Nauk SSSR, vol. 165, no. 3, 471–473 (1965).
Loday J.-L., “Une version non commutative des algèbres de Lie: les algèbres de Leibniz,” Enseign. Math., vol. 39, no. 3–4, 269–293 (1993).
Balavoine D., “Déformations et rigidité géométrique des algebras de Leibniz,” Comm. Algebra, vol. 24, no. 3, 1017–1034 (1996).
Hochschild G. and Serre J-P., “Cohomology of Lie algebras,” Ann. Math., vol. 57, 591–603 (1953).
Ancochea Bermúdez J. M. and Campoamor-Stursberg R., “Cohomologically rigid solvable Lie algebras with a nilradical of arbitrary characteristic sequence,” Linear Algebra Appl., vol. 488, 135–147 (2016).
Khalkulova Kh. A. and Abdurasulov K. K., “Solvable Lie algebras with maximal dimension of complementary space to nilradical,” Uzbek Math. J., vol. 1, 90–98 (2018).
Ancochea Bermúdez J. M. and Campoamor-Stursberg R., “On a complete rigid Leibniz non-Lie algebra in arbitrary dimension,” Linear Algebra Appl., vol. 438, no. 8, 3397–3407 (2013).
Author information
Authors and Affiliations
Corresponding authors
Additional information
To Academician Yuri Leonidovich Ershov on his 80th birthday.
Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 641–653.
Rights and permissions
About this article
Cite this article
Mamadaliev, U.K., Omirov, B.A. Cohomologically Rigid Solvable Leibniz Algebras with Nilradical of Arbitrary Characteristic Sequence. Sib Math J 61, 504–515 (2020). https://doi.org/10.1134/S003744662003012X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S003744662003012X