W-algebras and Duflo isomorphism

On Isomorphism of Simplicial Complexes and Their Related Algebras

On the Duflo Formula for L∞-algebras and Q-manifolds

We prove a direct analogue of the classical Duflo formula in the case of L∞algebras. We conjecture an analogous formula in the case of an arbitrary Q-manifold. When G is a compact connected Lie group, the Duflo theorem for the Q-manifold (ΠTG, dDR) is exactly the Duflo theorem for the Lie algebra g = LieG. The corresponding theorem for the Q-manifold (ΠTM,dDR), where M is an arbitrary smooth ma...

W ∗-algebras and integration

We present the mathematical setting of the theory of W ∗-algebras, including the Tomita– Takesaki modular theory, the Connes–Araki relative modular theory, the theory of W ∗dynamical systems (with derivations, liouvilleans, and crossed products), and noncommutative integration up to the Falcone–Takesaki theory of noncommutative Lp(N ) spaces. We pay special attention to abstract algebraic formu...

Linearization of W algebras and W superalgebras

In a recent paper, the authors have shown that the secondary reduction of W-algebras provides a natural framework for the linearization of W-algebras. In particular, it allows in a very simple way the calculation of the linear algebra W(G, H) ≥0 associated to a wide class of W(G,H) algebras, as well as the expression of the W generators of W(G,H) in terms of the generators of W(G, H) ≥0. In thi...

q-deformed W-algebras and elliptic algebras

The elliptic algebra Aq,p(ŝl(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 WN algebra, are constructed. The operators t(z) also close an exchange algebra when (−p1/2)NM = q−c−N for M ∈ Z. It becomes Abelian when in addition p = qNh where h is a non-zero integer. The Poisson structures...