This article is cited in 7 papers

MATHEMATICS

On parasasakian structures on five-dimensional Lie algebras

N. K. Smolentsev, I. Y. Shagabudinova

Kemerovo State University, Kemerovo, Russia

Abstract: Para-Sasakian structures on five-dimensional contact Lie algebras $\mathfrak{g}$ with nonzero center are considered. Such Lie algebras are central extensions of the four-dimensional para-Kähler Lie algebras $(\mathfrak{h},\omega)$. In this paper, a classification of five-dimensional para-Sasakian Lie algebras with a nontrivial center is proposed, based on the classification of para-Kähler structures $J$ on symplectic Lie algebras $(\mathfrak{h},\omega)$.

Keywords: para-complex structure, left-invariant para-Kahler structure, para-contact structure, left-invariant para-Sasakian structures.

UDC: 514.76

MSC: 53C15, 53D10, 53C25, 53C50

Received: 08.06.2020

DOI: 10.17223/19988621/69/4

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