scholarly journals Quadratic and symplectic structures on 3-(Hom)–ρ-Lie algebras

2021 ◽  
Vol 62 (8) ◽  
pp. 081702
Author(s):  
Zahra Bagheri ◽  
Esmaeil Peyghan
Keyword(s):  
Lie Algebras ◽  
Symplectic Structures

Poisson and symplectic structures on Lie algebras. I

1997 ◽  
Vol 22 (3) ◽  
pp. 191-211 ◽  
Author(s):  
D.V. Alekseevsky ◽  
A.M. Perelomov
Keyword(s):  
Lie Algebras ◽  
Symplectic Structures

scholarly journals Symplectic structures on quadratic Lie algebras

2007 ◽  
Vol 316 (1) ◽  
pp. 174-188 ◽  
Author(s):  
Ignacio Bajo ◽  
Saïd Benayadi ◽  
Alberto Medina
Keyword(s):  
Lie Algebras ◽  
Symplectic Structures

scholarly journals Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds

2019 ◽  
Vol 31 (3) ◽  
pp. 563-578
Author(s):  
Marcos Origlia
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Type I ◽  
Symplectic Structures ◽  
Locally Conformal

Abstract We study Lie algebras of type I, that is, a Lie algebra {\mathfrak{g}} where all the eigenvalues of the operator {\operatorname{ad}_{X}} are imaginary for all {X\in\mathfrak{g}} . We prove that the Morse–Novikov cohomology of a Lie algebra of type I is trivial for any closed 1-form. We focus on locally conformal symplectic structures (LCS) on Lie algebras of type I. In particular, we show that for a Lie algebra of type I any LCS structure is of the first kind. We also exhibit lattices for some 6-dimensional Lie groups of type I admitting left invariant LCS structures in order to produce compact solvmanifolds equipped with an invariant LCS structure.

scholarly journals Complex symplectic structures on Lie algebras

2021 ◽  
Vol 225 (6) ◽  
pp. 106585
Author(s):  
Giovanni Bazzoni ◽  
Marco Freibert ◽  
Adela Latorre ◽  
Benedict Meinke
Keyword(s):  
Lie Algebras ◽  
Symplectic Structures ◽  
Complex Symplectic

scholarly journals Symplectic structures on the filiform Lie algebras

2001 ◽  
Vol 156 (1) ◽  
pp. 15-31 ◽  
Author(s):  
J.R. Gómez ◽  
A. Jiménez-Merchán ◽  
Y. Khakimdjanov
Keyword(s):  
Lie Algebras ◽  
Symplectic Structures ◽  
Filiform Lie Algebras
Sign in / Sign up

Export Citation Format

Share Document