A compatible left-symmetric algebra is a pair of left-symmetric algebras satisfying that any linear combination of the two left-symmetric products is a left-symmetric product.We construct a bialgebra theory of compati...A compatible left-symmetric algebra is a pair of left-symmetric algebras satisfying that any linear combination of the two left-symmetric products is a left-symmetric product.We construct a bialgebra theory of compatible left-symmetric algebras as an analogue of a Lie bialgebra.They can also be regarded as a"compatible version"of leftsymmetric bialgebras,that is,a pair of left-symmetric bialgebras satisfying that any linear combination of the two left-symmetric bialgebras is still a left-symmetric bialgebra.Many properties of compatible left-symmetric bialgebras as the"compatible version"of the corresponding properties of left-symmetric bialgebras are presented.In particular,there is a coboundary compatible left-symmetric bialgebra theory and an S-equation,which is an analogue of the classical Yang-Baxter equations in Lie algebras.展开更多
基金Supported by the Meritocracy Research Funds of China West Normal University and the Fundamental Research Funds of China West Normal University(17C048,17YC392)by Scientific Research Fund of Sichuan Provincial Education Department(17AZ0378).
文摘A compatible left-symmetric algebra is a pair of left-symmetric algebras satisfying that any linear combination of the two left-symmetric products is a left-symmetric product.We construct a bialgebra theory of compatible left-symmetric algebras as an analogue of a Lie bialgebra.They can also be regarded as a"compatible version"of leftsymmetric bialgebras,that is,a pair of left-symmetric bialgebras satisfying that any linear combination of the two left-symmetric bialgebras is still a left-symmetric bialgebra.Many properties of compatible left-symmetric bialgebras as the"compatible version"of the corresponding properties of left-symmetric bialgebras are presented.In particular,there is a coboundary compatible left-symmetric bialgebra theory and an S-equation,which is an analogue of the classical Yang-Baxter equations in Lie algebras.
