72 citations · 134 across the 17 of their papers we have counts for
12 papers · 1 filter
Formal symplectic geometry for Leibniz algebras
K. Uchino
We study a formal symplectic geometry for anticyclic Leibniz operad and its Koszul dual operad.
Derived bracket construction and anti-cyclic subcomplex of Leibniz (co)homology complex
K. Uchino
An arbitrary Leibniz algebra can be embedded in a differential graded Lie algebra via the derived bracket construction. Such an embedding is called a derived bracket representation…
Derived bracket construction up to homotopy and Schroder numbers
K. Uchino
We will introduce the notion of higher derived bracket construction in the category of operads and prove that the higher derived bracket construction of Lie operad is equivalent to…
On distributive laws in derived bracket construction and homotopy theory of derived bracket Leibniz algebras
K. Uchino
We introduce a new type of algebra, which is called a Lie-Leibniz algebra. This concept is an abstraction of derived bracket construction. It will be proved that the operad of Lie-…
Leibniz algebras on symplectic plane and cohomological vector fields
K. Uchino
By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on non…
Noncommutative Poisson brackets on Loday algebras and related deformation quantization
Kyousuke Uchino
Given a Lie algebra, there uniquely exists a Poisson algebra which is called a Lie-Poisson algebra over the Lie algebra. We will prove that given a Loday/Leibniz algebra there exis…