Related papers: Conjugacy classes in Weyl groups and q-W algebras

Quadratic Poisson brackets on associative algebras are studied. Such a bracket compatible with the multiplication is related to a differentiation in tensor square of the underlying algebra. Jacobi identity means that this differentiation…

Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of…

Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We…

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…

We investigate the Banach Lie groupoids and inverse semigroups naturally associated to W*-algebras. We also present statements describing relationship between these groupoids and the Banach Poisson geometry which follows in the canonical…

We study certain representations of quantum toroidal $\mathfrak{gl}_1$ algebra for $q=t$. We construct explicit bosonization of the Fock modules $\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it is naturally…

In this paper we realize the supersymmetric classical $W$-algebras $\mathcal{W}(\overline{\mathfrak{gl}}(n+1|n))$ and $\mathcal{W}(\overline{\mathfrak{gl}}(n|n))$ as differential algebras generated by the coefficients of a monic…

We prove that an invariant subalgebra A_n^W of the Weyl algebra A_n is a Galois order over an adequate commutative subalgebra \Gamma when W is a two-parameters irreducible unitary reflection group G(m,1,n), m\geq 1, n\geq 1, including the…

Hsiang algebras are a class of nonassociative algebra defined in terms of a relation quartic in elements of the algebra. This class arises naturally in relation to the construction of real algebraic minimal cones. Additionally, Hsiang…

By calculating inequivalent classical r-matrices for the $gl(2,\mathbb{R})$ Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE)), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the…

For an algebraically closed field $K$, we investigate a class of noncommutative $K$-algebras called connected quantized Weyl algebras. Such an algebra has a PBW basis for a set of generators $\{x_1,\dots,x_n\}$ such that each pair satisfies…

We introduce and develop a structure theory of a new class of noncommutative rings - Galois orders, that generalize classical orders in noncommutative rings. Galois orders realized as certain subrings of invariants in skew semigroup rings.…

Let $O$ be a closed Poisson conjugacy class of the complex algebraic Poisson group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix. Denote by $T$ the maximal torus of diagonal matrices in GL(n). With every $a\in O\cap…

Infinite-dimensional Galilean conformal algebras can be constructed by contracting pairs of symmetry algebras in conformal field theory, such as $W$-algebras. Known examples include contractions of pairs of the Virasoro algebra, its $N=1$…

The loop group $G((z^{-1}))$ of a simple complex Lie group $G$ has a natural Poisson structure. We introduce a natural family of Poisson commutative subalgebras $\overline{{\mathbf{B}}}(C) \subset \mathcal{O}(G((z^{-1}))$ depending on the…

To each simple Lie algebra g and an element w of the corresponding Weyl group De Concini, Kac and Procesi associated a subalgebra U^w_- of the quantized universal enveloping algebra U_q(g), which is a deformation of the universal enveloping…

We introduce a new family of Poisson vertex algebras $\mathcal{W}(\mathfrak{a})$ analogous to the classical $\mathcal{W}$-algebras. The algebra $\mathcal{W}(\mathfrak{a})$ is associated with the centralizer $\mathfrak{a}$ of an arbitrary…

We review the construction of Drinfeld-Sokolov type hierarchies and classical W-algebras in a Hamiltonian symmetry reduction framework. We describe the list of graded regular elements in the Heisenberg subalgebras of the nontwisted loop…

Generalised almost complex structures $\mathcal J$ on transitive Courant algebroids $E$ are studied in terms of their components with respect to a splitting $E\cong TM \oplus T^*M \oplus \mathcal G$, where $M$ denotes the base of $E$ and…

We study the deformation complex of the dg wheeled properad of $\mathbb{Z}$-graded quadratic Poisson structures and prove that it is quasi-isomorphic to the even M. Kontsevich graph complex. As a first application we show that the…