Complex nilpotent Lie algebras of dimension 7 which are not derived from others.
Francisco J. Echarte, José R. Gómez, Juan Núñez (1994)
Extracta Mathematicae
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Francisco J. Echarte, José R. Gómez, Juan Núñez (1994)
Extracta Mathematicae
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Malliavin, Marie Paule (1994)
Beiträge zur Algebra und Geometrie
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Baguis, P., Stavracou, T. (2002)
International Journal of Mathematics and Mathematical Sciences
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Pilar Benito, Daniel de-la-Concepción (2014)
Commentationes Mathematicae Universitatis Carolinae
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Any nilpotent Lie algebra is a quotient of a free nilpotent Lie algebra of the same nilindex and type. In this paper we review some nice features of the class of free nilpotent Lie algebras. We will focus on the survey of Lie algebras of derivations and groups of automorphisms of this class of algebras. Three research projects on nilpotent Lie algebras will be mentioned.
Schneider, Csaba (2005)
Experimental Mathematics
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Zhiqi Chen (2011)
Czechoslovak Mathematical Journal
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Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and the Hamiltonian operators in formal variational calculus. In this note we prove that the underlying Lie algebras of quadratic Novikov algebras are 2-step nilpotent. Moreover, we give the classification up to dimension .
Hernández, I., Peniche, R. (2008)
International Journal of Mathematics and Mathematical Sciences
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Benayed, Miloud, Souidi, El Mamoun (1998)
The New York Journal of Mathematics [electronic only]
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Kenny De Commer (2015)
Banach Center Publications
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On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
Liping Sun, Wende Liu (2017)
Open Mathematics
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According to the classification by Kac, there are eight Cartan series and five exceptional Lie superalgebras in infinite-dimensional simple linearly compact Lie superalgebras of vector fields. In this paper, the Hom-Lie superalgebra structures on the five exceptional Lie superalgebras of vector fields are studied. By making use of the ℤ-grading structures and the transitivity, we prove that there is only the trivial Hom-Lie superalgebra structures on exceptional simple Lie superalgebras....
Daniel Beltiţă (1999)
Studia Mathematica
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A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.