论文标题
Koszul-Vinberg结构和左对称代数的兼容结构
Koszul-Vinberg structures and compatible structures on left-symmetric algebroids
论文作者
论文摘要
In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and show that a Koszul-Vinberg-Nijenhuis structure gives rise to a hierarchy of Koszul-Vinberg structures.我们介绍了$ {\ rmkvΩ} $的概念 - 结构，伪 - hessian-nijenhuis结构和互补的对称$ 2 $ - KOSZUL-VINBERG结构上的左对称代数上的结构，这是$ {\ rm prom prom propuly and symSteriors-prouns-prouns-prouns-prouns-prouns-prouns symSterriers and symSterries-nij-sustem-nij-sustem-nij-rucies-susteriers-nij-sustem-nij-sustem-nij-sustem-nij-susternher， $ 2 $ - 泊松结构的形式。我们还研究了这些各种结构之间的关系。
In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and show that a Koszul-Vinberg-Nijenhuis structure gives rise to a hierarchy of Koszul-Vinberg structures. We introduce the notions of ${\rm KVΩ}$-structures, pseudo-Hessian-Nijenhuis structures and complementary symmetric $2$-tensors for Koszul-Vinberg structures on left-symmetric algebroids, which are analogues of ${\rm PΩ}$-structures, symplectic-Nijenhuis structures and complementary $2$-forms for Poisson structures. We also study the relationships between these various structures.
