Related papers: BFV-complex and higher homotopy structures

Complex supermanifold structures being deformations of the exterior algebra of a holomorphic vector bundle, have been parametrized by orbits of a group on non-abelian cohomology by P. Green. For the case of odd dimension $4$ and $5$ an…

For M a closed, connected, oriented manifold, we obtain the Batalin-Vilkovisky (BV) algebra of its string topology through homotopy-theoretic constructions on its based loop space. In particular, we show that the Hochschild cohomology of…

We construct explicitly a class of coboundary Poisson-Lie structures on the group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra $W_n$…

We give the analogue for Hopf algebras of the polyuble Lie bialgebra construction by Fock and Rosli. By applying this construction to the Drinfeld-Jimbo quantum group, we obtain a deformation quantization $\mathbb{C}_\hslash[(N \backslash…

We settle several questions about the theory of universal deformation quantization of Lie bialgebras by giving their complete classification up to homotopy equivalence. An important new technical ingredient introduced in this paper is an…

The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost…

An anologue of the Calabi invariant for Poisson manifolds is considered. For any Poisson manifold $P$, the Poisson bracket on $C^{\infty}(P)$ extends to a Lie bracket on the space $\Omega^{1}(P)$ of all differential one-forms, under which…

We study holomorphic geometric structures on non-K\"ahler compact complex manifolds with trivial canonical line bundle. For Vaisman Calabi-Yau manifolds we prove that all holomorphic geometric structures of affine type on them are locally…

We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…

Integrable deformations of a class of Rikitake dynamical systems are constructed by deforming their underlying Lie-Poisson Hamiltonian structures, which are considered linearizations of Poisson--Lie structures on certain (dual) Lie groups.…

Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra, called big algebra, attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are…

We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy…

Jacobi structures are known to generalize Poisson structures, encompassing symplectic, cosymplectic, and Lie-Poisson manifolds. Notably, other intriguing geometric structures -- such as contact and locally conformal symplectic manifolds --…

We introduce the notion of a conformally Fedosov structure and construct an associated Cartan connection. When an appropriate curvature vanishes, this allows us to construct a family of natural differential complexes akin to the BGG…

In 1995, Dan Guan constructed examples of non-Kahler, simply-connected holomorphically symplectic manifolds. An alternative construction, using the Hilbert scheme of Kodaira-Thurston surface, was given by F. Bogomolov. We investigate…

Poisson structures related with the affine Courant type algebroid are analyzed, including \ those related with cotangent bundles on Lie group manifolds. A special attantion is paid to Courant type algebroids and related R-structures \ on…

We realize explicitly the well-known additive decomposition of the Hochschild cohomology ring of a group algebra in the elements level. As a result, we describe the cup product, the Batalin-Vilkovisky operator and the Lie bracket in the…

This is an extended example of the study of mirror symmetry via log schemes and the discrete Legendre transform on affine manifolds, introduced by myself and Bernd Siebert in "Mirror Symmetry via Logarithmic Degeneration Data I"…

We introduce the notions of generalised (bi-)Hamiltonian structures which generalise naturally the (bi-)Hamiltonian structures of evolutionary partial differential equations. In the hydrodynamic case, these structures are characterised in…

This paper reinterprets the symmetries of equivariant Khovanov homology, discovered by Khovanov and Sano, within the Batalin-Vilkovisky (BV) formalism. We identify the Shumakovitch operator $\hat{\nu}$ as a BV Laplacian whose nilpotency, a…