Wall crossing, discrete attractor flow and Borcherds algebra.
Ward identities from recursion formulas for correlation functions in conformal field theory
A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find -point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg and free...
Weak c*-Hopf algebras: the coassociative symmetry of non-integral dimensions
By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C*-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplicative unitary of Baaj and Skandalis with a partial isometry. The algebraic properties, the existence of...
Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples
Let G be a finite group. Consider the algebra A of all complex functions on G (with pointwise product). Define a coproduct Δ on A by Δ(f)(p,q) = f(pq) where f ∈ A and p,q ∈ G. Then (A,Δ) is a Hopf algebra. If G is only a groupoid, so that the product of two elements is not always defined, one still can consider A and define Δ(f)(p,q) as above when pq is defined. If we let Δ(f)(p,q) = 0 otherwise, we still get a coproduct on A, but Δ(1) will no longer be the identity in A ⊗ A. The pair (A,Δ)...
Weak polynomial identities and their applications
Let be an associative algebra over a field generated by a vector subspace . The polynomial of the free associative algebra is a weak polynomial identity for the pair if it vanishes in when evaluated on . We survey results on weak polynomial identities and on their applications to polynomial identities and central polynomials of associative and close to them nonassociative algebras and on the finite basis problem. We also present results on weak polynomial identities of degree three....
Weak Polynomial Identities for M1,1(E)
* Partially supported by Universita` di Bari: progetto “Strutture algebriche, geometriche e descrizione degli invarianti ad esse associate”.We compute the cocharacter sequence and generators of the ideal of the weak polynomial identities of the superalgebra M1,1 (E).
Wedderburnzerlegung für Jordan-Paare.
Weight multiplicity polynomials for affine Kac-Moody algebras of type
Weighted Aztec diamond graphs and the Weyl character formula.
Weitzenböck Formula on Lie Algebroids
A Weitzenböck formula for the Laplace-Beltrami operator acting on differential forms on Lie algebroids is derived.
When is a quantum space not a group?
We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as properties...
Whittaker models, nilpotent orbits and the asymptotics of Harish-Chandra modules
Whittaker vectors and associated varieties.
Wigner quantization of Hamiltonians describing harmonic oscillators coupled by a general interaction matrix.
Wild automorphisms of nilpotent-by-abelian Lie algebras.
Witt algebra and the curvature of the Heisenberg group
The aim of this paper is to determine explicitly the algebraic structure of the curvature algebra of the 3-dimensional Heisenberg group with left invariant cubic metric. We show, that this curvature algebra is an infinite dimensional graded Lie subalgebra of the generalized Witt algebra of homogeneous vector fields generated by three elements.