Related papers: Transposed Poisson structures on Virasoro-type alg…
Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic…
We construct and study non-finitely graded Lie algebras $\mathcal{HV}(a,b;\epsilon)$ related to Heisenberg-Virasoro type Lie algebras, where $a,b$ are complex numbers, and $\epsilon = \pm 1$. Using combinatorial techniques, we completely…
We classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.
In this paper, Lie bialgebra structures on generalized Heisenberg-Virasoro algebra $\mathfrak{L}$ are considered. Also, $H^1({\mathfrak{L}} ,\mathfrak{L}\bigotimes\mathfrak{L})$ is given explicitly. Moreover, it is proved that all Lie…
We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra structure on the reduced cyclic homology. Under the…
In this paper, we study a new kind of vertex operator algebra related to the twisted Heisenberg-Virasoro algebra, which we call the twisted Heisenberg-Virasoro vertex operator algebra, and its modules. Specifically, we present some results…
A family of Poisson structures, parametrised by an arbitrary odd periodic function $\phi$, is defined on the space $\cW$ of twisted polygons in $\RR^\nu$. Poisson reductions with respect to two Poisson group actions on $\cW$ are described.…
This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the…
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL(2). The nontrivial…
We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.
In this paper, we determine all simple restricted modules over the mirror Heisenberg-Virasoro algebra ${\mathfrak{D}}$, and the twisted Heisenberg-Virasoro algebra $\bar\mathfrak{D}$ with nonzero level. As applications, we characterize…
In this article, the Virasoro-type reduction and the corresponding inverse reductions are established for W-algebras associated with classical Lie type and nilpotent orbits of height two. Moreover, these results are lifted to the universal…
We define the q-deformed Gelfand-Dickey bracket on the space of q-pseudodifference symbols which agrees with the Poisson Virasoro algebra of E.Frenkel and N.Reshetikhin and its generalizations and prove its uniqueness (in a natural class of…
In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra.…
We construct and classify all Poisson structures on quasimodular forms that extend the one coming from the first Rankin-Cohen bracket on the modular forms. We use them to build formal deformations on the algebra of quasimodular forms.
We review nonabelian Poisson structures on affine and projective spaces over $\mathbb{C}$. We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{n-1}$ for $n>2$. These nonabelian Poisson structures depend…
We study $\mathbb Z_2$-graded Poisson structures defined on $\mathbb Z_2$-graded commutative polynomial algebras. In small dimensional cases, we exhibit classifications of such Poisson structures, obtain the associated Poisson $\mathbb…
Double Poisson structures (a la Van den Bergh) on commutative algebras are studied; the main result shows that there are no non-trivial such structures on polynomial algebras of Krull dimension greater than one. For a general commutative…
We describe graded contractions of Virasoro algebra. The highest weight representations of Virasoro algebra are constructed. The reducibility of representations is analysed. In contrast to standart representations the contracted ones are…
Let $\mathfrak g(G,\lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $\lambda\neq-1$ and an additive subgroup $G$ of $\mathbb C$. For a total order on $G$ that is compatible with addition,…