Symplectic Lie algebras with degenerate center
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DOI: 10.1016/j.jalgebra.2018.11.038
Abstract: Every symplectic Lie algebra with degenerate (including non-abelian nilpotent symplectic Lie algebras) has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic… read more here.
Keywords: lie; degenerate center; lie algebras; symplectic lie ... See more keywords
Quadratic symplectic Lie superalgebras with a filiform module as an odd part
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DOI: 10.1063/5.0142935
Abstract: The present work studies deeply quadratic symplectic Lie superalgebras, obtaining, in particular, that they are all nilpotent. Consequently, we provide classifications in low dimensions and identify the double extensions that maintain symplectic structures. By means… read more here.
Keywords: quadratic symplectic; lie superalgebras; superalgebras filiform; symplectic lie ... See more keywords
On k-para-Kähler Lie algebras, a subclass of k-symplectic Lie algebras
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DOI: 10.1080/00927872.2021.1922697
Abstract: Abstract k-Para-Kähler Lie algebras are a generalization of para-Kähler Lie algebras (k = 1) and constitute a subclass of k-symplectic Lie algebras. In this paper, we show that the characterization of para-Kähler Lie algebras as left symmetric… read more here.
Keywords: lie; para hler; hler lie; lie algebras ... See more keywords
Flat symplectic Lie algebras
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DOI: 10.1080/00927872.2023.2209671
Abstract: Let $(G,\Omega)$ be a symplectic Lie group, i.e, a Lie group endowed with a left invariant symplectic form. If $\G$ is the Lie algebra of $G$ then we call $(\G,\omega=\Om(e))$ a symplectic Lie algebra. The… read more here.
Keywords: lie; lie group; lie algebras; symplectic lie ... See more keywords