2000/02/07 by T. A. Larsson, Larsson, T. A. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0002016
Corrected treatment of special 2-dim cocycles. Added section on div-free, Hamiltonian and contact subalgebras. 34 pages, Latex2e
openalex publication_date 2000/02/07 · arxiv created 2000/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dzhumadil'daev has classified all tensor module extensions of diff(N), the diffeomorphism algebra in N dimensions, and its subalgebras of divergence free, Hamiltonian, and contact vector fields. I review his results using explicit tensor notation. All of his generic cocycles are limits of trivial cocycles, and many arise from the Mickelsson-Faddeev algebra for gl(N). Then his results are extended to some non-tensor modules, including the higher-dimensional Virasoro algebras found by Eswara Rao/Moody and myself. Extensions of current algebras with d-dimensional representations are obtained by restriction from diff(N+d). This gives a connection between higher-dimensional Virasoro and Kac-Moody cocycles, and between Mickelsson-Faddeev cocycles for diffeomorphism and current algebras.