Displaying similar documents to “Dolbeault homotopy theory and compact nilmanifolds”

On compact symplectic and Kählerian solvmanifolds which are not completely solvable

Aleksy Tralle (1997)

Colloquium Mathematicae

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We are interested in the problem of describing compact solvmanifolds admitting symplectic and Kählerian structures. This was first considered in [3, 4] and [7]. These papers used the Hattori theorem concerning the cohomology of solvmanifolds hence the results obtained covered only the completely solvable case}. Our results do not use the assumption of complete solvability. We apply our methods to construct a new example of a compact symplectic non-Kählerian solvmanifold.

Nilpotent control systems.

Elisabeth Remm, Michel Goze (2002)

Revista Matemática Complutense

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We study the class of matrix controlled systems associated to graded filiform nilpotent Lie algebras. This generalizes the non- linear system corresponding to the control of the trails pulled by car.

Some necessary and sufficient conditions for nilpotent n -Lie superalgebras

Baoling Guan, Liangyun Chen, Yao Ma (2014)

Czechoslovak Mathematical Journal

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The paper studies nilpotent n -Lie superalgebras over a field of characteristic zero. More specifically speaking, we prove Engel’s theorem for n -Lie superalgebras which is a generalization of those for n -Lie algebras and Lie superalgebras. In addition, as an application of Engel’s theorem, we give some properties of nilpotent n -Lie superalgebras and obtain several sufficient conditions for an n -Lie superalgebra to be nilpotent by using the notions of the maximal subalgebra, the weak ideal...

Lefschetz coincidence numbers of solvmanifolds with Mostow conditions

Hisashi Kasuya (2014)

Archivum Mathematicum

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For any two continuous maps f , g between two solvmanifolds of the same dimension satisfying the Mostow condition, we give a technique of computation of the Lefschetz coincidence number of f , g . This result is an extension of the result of Ha, Lee and Penninckx for completely solvable case.

Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups

Mohammed Guediri, Mona Bin-Asfour (2014)

Archivum Mathematicum

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The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if , is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group N , then the restriction of , to the center of the Lie algebra of N is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group...