ﻻ يوجد ملخص باللغة العربية
We construct double cross biproduct and bi-cycle bicrossproduct Lie bialgebras from braided Lie bialgebras. The main result generalizes Majids matched pairs of Lie algebras, Drinfelds quantum double, and Masuokas cross product Lie bialgebras.
We study (quasi-)twilled pre-Lie algebras and the associated $L_infty$-algebras and differential graded Lie algebras. Then we show that certain twisting transformations on (quasi-)twilled pre-Lie algbras can be characterized by the solutions of Maure
For any integer $d$ we introduce a prop $RHra_d$ of oriented ribbon hypergraphs (in which edges can connect more than two vertices) and prove that it admits a canonical morphism of props, $$ Holieb_d^diamond longrightarrow RHra_d, $$ $Holieb_d^diamon
We describe $L_infty$-algebras governing homotopy relative Rota-Baxter Lie algebras and triangular $L_infty$-bialgebras, and establish a map between them. Our formulas are based on a functorial approach to Voronovs higher derived brackets construction which is of independent interest.
The $n$-Lie bialgebras are studied. In Section 2, the $n$-Lie coalgebra with rank $r$ is defined, and the structure of it is discussed. In Section 3, the $n$-Lie bialgebra is introduced. A triple $(L, mu, Delta)$ is an $n$-Lie bialgebra if and only i
We introduce fusion bialgebras and their duals and systematically study their Fourier analysis. As an application, we discover new efficient analytic obstructions on the unitary categorification of fusion rings. We prove the Hausdorff-Young inequalit