Related papers: The universal envelope of the topological closed s…
We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra…
Let $M$ be an oriented manifold and let $\frak N$ be a set consisting of oriented closed manifolds of the same odd dimension. We consider the topological space $G_{\frak N, M}$ of commutative diagrams. Each commutative diagram consists of a…
By using cocycle deformation, we construct a certain class of Hopf algebras, containing the quantized enveloping algebras and their analogues, from what we call pre-Nichols algebras. Our construction generalizes in some sense the known…
In this paper, we arrive from different starting points at the conclusion that the symmetry given by an action of the Grothendieck-Teichmueller group GT on the so called extended moduli space of string theory can not be physical - in the…
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we…
Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…
We construct an integral form for the universal enveloping algebra of the Onsager algebra and an explicit integral basis for this integral form. We also formulate straightening identities among some products of basis elements.
We propose a simple method for constructing representations of (super)conformal and nonlinear W-type algebras in terms of their subalgebras and corresponding Nambu-Goldstone fields. We apply it to N=2 and N=1 superconformal algebras and…
Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations…
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
We construct a Poisson algebra of brane currents from a QP-manifold (alias symplectic $L_\infty$-algebroid), and show their Poisson brackets take a universal geometric form. This generalises a result of Alekseev and Strobl on string…
We introduce the notion of a non--linear Lie conformal superalgebra and prove a PBW theorem for its universal enveloping vertex algebra. We also show that conversely any graded freely generated vertex algebra is the universal enveloping…
The elliptic algebra A_{q,p}(sl(N)_{c}) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W_N algebra, are constructed. The operators t(z)…
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
For any differential graded (DG for short) Poisson algebra $A$ given by generators and relations, we give a "formula" for computing the universal enveloping algebra $A^e$ of $A$. Moreover, we prove that $A^e$ has a Poincar\'e-Birkhoff-Witt…
It is well-known that a formal deformation of a commutative algebra ${\mathcal A}$ leads to a Poisson bracket on ${\mathcal A}$ and that the classical limit of a derivation on the deformation leads to a derivation on ${\mathcal A}$, which…
The space of local operators in the $Q$-cohomology of the holomorphic-topological supercharge in a four-dimensional $\mathcal{N}=2$ theory carries the structure of a Poisson vertex algebra. This note studies the Poisson vertex algebra…
The generalized deformed oscillator schemes introduced as unified frameworks of various deformed oscillators are proved to be equivalent, their unified representation leading to a correspondence between the deformed oscillator and the N=2…
The Poisson structure arising in the Hamiltonian approach to the rational Gaudin model looks very similar to the so-called modified Reflection Equation Algebra. Motivated by this analogy, we realize a braiding of the mentioned Poisson…
The Hopf dual $H^\circ$ of any Poisson Hopf algebra $H$ is proved to be a co-Poisson Hopf algebra provided $H$ is noetherian. Without noetherian assumption, it is not true in general. There is no nontrivial Poisson Hopf structure on the…