Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac–Moody bialgebras. Doing so, we obtain many new examples of infinite-dimensional braided-Lie bialgebras. We analyze further the case of untwist...

In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset U ⊂ V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex ...

We introduce a dual notion of the Poisson algebra, called transposed by exchanging roles two binary operations in Leibniz rule defining algebra. The algebra shares common properties and arises naturally from Novikov-Poisson taking commutator Lie Novikov Consequently, classic construction commutative with commuting derivations similarly applies to More broadly, captures algebraic structures when...

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2 : n;ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2 : n;ω2) with a Block algebra. W...