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 way from the W*-algebra structure.
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18 results for “W-algebra”
Study examines linear Poisson structures tied to W*-algebras.
problem Understanding fiber-wise linear Poisson structures related to W*-algebras.
method Investigates structures defined by W*-algebra structure and shows their arrangement in a short exact sequence of VB-groupoids.
result Fiber-wise linear Poisson structures are arranged in a short exact sequence of VB-groupoids.
We prove that the classical -algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical -algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic sub…
Study of coloured invariants of torus knots using algebras.
problem Understanding coloured invariants of torus knots .
method Representation theory of principal affine algebras and asymptotic weight multiplicities.
result Limits of renormalized invariants are equal to characters of algebra modules.
Constructs algebraic classical W-algebras and Frobenius manifolds.
problem Describes algebraic structures associated with semisimple Lie groups.
method Bihamiltonian structure, Poisson pencil, dispersionless limit.
result Uniform construction of algebraic Frobenius manifolds.
We obtain polynomial Frobenius manifolds from classical -algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.
We obtain algebraic Frobenius manifolds from classical -algebras associated to subregular nilpotent elements in simple Lie algebras of type where is even and . The resulting Frobenius manifolds are certain hypersurfaces in the total spaces of semiuniversal deformation of simple hypersurface singularit…
In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a -algebra. In particular the complex analytic manifold structure of these objects is investigated. The expressions on the Lie brackets for A and related algebroids are given in nonc…
Study Higgs bundles on CP1 with specific singularities, linking fixed points to W-algebra representations.
problem Analyzing Higgs bundles with irregular singularities and their fixed points.
method Introduced a -action on and classified its fixed points.
result Found a 1-1 correspondence between fixed points and certain W-algebra representations.
Combines higher complex structures with flat connections to link to -algebras.
problem Linking higher complex structures to -algebras via flat connections.
method Introduces -parabolic connections and studies their curvature.
result Establishes a direct link between flat connections and higher complex structures.
Constructs bihamiltonian structures from Lie algebras for specific types of nilpotent elements.
problem Constructing bihamiltonian structures from Lie algebras.
method Using classical -algebras and non-regular nilpotent elements of semisimple type.
result Leading terms define Dubrovin-Frobenius manifolds and calculate central invariants.
The quadratic WDVV solution math.DG
We calculate explicitly the quadratic solution to the WDVV equations corresponds to the quasi-Coxeter conjugacy class using the associated classical -algebra.
If V and W are varieties of algebras such that any V-algebra A has a reduct U(A) in W, there is a forgetful functor U: V->W that acts by A |-> U(A) on objects, and identically on homomorphisms. This functor U always has a left adjoint F: W->V by general considerations. One calls F(B) the V-algebra freely generated by t…
Differential structure on partial isometries over Grassmannian constructed.
problem No specific problem stated; abstract focuses on method and result.
method Construction of differential structure on partial isometries over restricted Grassmannian.
result Set of partial isometries over restricted Grassmannian becomes a Banach Lie groupoid.
I will explain my joint paper `Instantons moduli spaces and W-algebras' with A.Braverman, M.Finkelberg, arXiv:1406.2381. I will concentrate on the geometric part, that is a study of perverse sheaves on instanton moduli spaces. I place a particular emphasize on the hyperbolic restriction functor and stable envelop, whic…
Positive energy representations of affine algebras and Stokes matrices of the affine Toda equationsmath.DG
Constructs positive energy representations from Toda equations Stokes data.
problem Creating positive energy representations of affine algebras.
method Using Stokes data of tt*-Toda equations to construct representations.
result Illustrates construction with examples in conformal field theory.
String theory connects lattice models, links, and geometric Langlands.
problem Connecting lattice models, links, and geometric Langlands.
method T-duality and worldvolume theories in string theory.
result Unified understanding of various mathematical concepts.
Formula for colored invariants of torus knots linked to algebras.
problem Calculating colored invariants of torus knots.
method Generalizing Morton's work, formula derivation for invariants and their limits to characters.
result Limits of invariants are essentially characters of algebras, modular up to factors.