Search results for "Loop group"
showing 7 items of 7 documents
Structure of Kac-Moody groups
2008
For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,
Transportation cost inequalities on path and loop groups
2005
AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).
Integration by parts for heat measures over loop groups
1999
Abstract The formula of integration by parts for heat measures over a loop group established by B. Driver is revesited through an alternative approach to this result. We shall first establish directly the integration by parts formula over an unimodular Lie group (which will be the finite product of a compact Lie group with a correlated metric), using the concept of tangent processes. A new expression for Ricci tensor will enable us the passage to the limit.
De Rham–Hodge–Kodaira Operator on Loop Groups
1997
AbstractWe consider a based loop group Le(G) over a compact Lie groupG, endowed with its pinned Wiener measureν(the law of the Brownian bridge onG) and we shall calculate the Ricci curvature for differentialn-forms over Le(G). A type of Bochner–Weitzenböck formula for general differentialn-forms (or Shigekawa identity) will be established.
Fokker–Planck equation with respect to heat measures on loop groups
2011
Abstract The Dirichlet form on the loop group L e ( G ) with respect to the heat measure defines a Laplacian Δ DM on L e ( G ) . In this note, we will use Wasserstein distance variational method to solve the associated heat equation for a given data of finite entropy.
Hamilton–Jacobi semi-groups in infinite dimensional spaces
2006
AbstractLet (X,ρ) be a Polish space endowed with a probability measure μ. Assume that we can do Malliavin Calculus on (X,μ). Let d:X×X→[0,+∞] be a pseudo-distance. Consider QtF(x)=infy∈X{F(y)+d2(x,y)/2t}. We shall prove that QtF satisfies the Hamilton–Jacobi inequality under suitable conditions. This result will be applied to establish transportation cost inequalities on path groups and loop groups in the spirit of Bobkov, Gentil and Ledoux.
Equivariant cohomology, Fock space and loop groups
2006
Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.