Research Specifications

Home \Some remarks on invariant ...
Title
Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups
Type of Research Article
Keywords
Poisson quasi-Nijenhuis structures; Lie bialgebras and coboundary Lie bialgebras; Generalized complex structures.
Abstract
We study right-invariant (respectively, left-invariant) Poisson quasi-Nijenhuis structures on a Lie group G and introduce their infinitesimal counterpart, the so-called r-qn structures on the corresponding Lie algebra g. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all r-qn structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between r-qn structures and the generalized complex structures on the Lie algebras g and also the solutions of modified Yang–Baxter equation (MYBE) on the double of Lie bialgebra g ⊕ g∗. The results are applied to some relevant examples.
Researchers Ghorbanali Haghighatdoost Bonab (First Researcher)، Zohreh Ravanpak (Second Researcher)، Adel Rezaei-Aghdam (Third Researcher)