Extensions of current groups on $S^3$ and the adjoint representations
Copyright policy )Extensions of current groups on $S^3$ and the adjoint representations
Let Omega^3(SU(n)) be the Lie group of based mappings from S^3 to SU(n). We construct a Lie group extension of Omega^3(SU(n)) for n>2 by the abelian group of the affine dual space of SU(n)-connections on S^3. In this article we give several improvement of J. Mickelsson's results in 1987, especially we give a precise description of the extension of those components that are not the identity component,. We also correct several argument about the extension of Omega^3(SU(2)) which seems not to be exact in Mickelsson's work, though his observation about the fact that the extension of Omega^3(SU(2)) reduces to the extension by Z_2 is correct. Then we shall investigate the adjoint representation of the Lie group extension of Omega^3(SU(n)) for n>2.
- Waseda University Japan
infinite dimensional Lie groups, Mathematics - Differential Geometry, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Infinite-dimensional Lie groups and their Lie algebras: general properties, Lie group extensions, Yang-Mills and other gauge theories in quantum field theory, 81R10, 22E67, Differential Geometry (math.DG), 81R10, Applications of Lie groups to the sciences; explicit representations, FOS: Mathematics, Loop groups and related constructions, group-theoretic treatment, 22E67, adjoint representations, 22E65, current groups
infinite dimensional Lie groups, Mathematics - Differential Geometry, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Infinite-dimensional Lie groups and their Lie algebras: general properties, Lie group extensions, Yang-Mills and other gauge theories in quantum field theory, 81R10, 22E67, Differential Geometry (math.DG), 81R10, Applications of Lie groups to the sciences; explicit representations, FOS: Mathematics, Loop groups and related constructions, group-theoretic treatment, 22E67, adjoint representations, 22E65, current groups
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