Extensions of diffeomorphism and current algebras

Details Extensions of diffeomorphism and current algebras Extensions of diffeomorphism and current algebras

2000-02-07

arxiv.org/abs/math-ph/0002016v2

Physics

Mathematical Physics

Corrected treatment of special 2-dim cocycles. Added section on div-free, Hamiltonian and contact subalgebras. 34 pages, Latex

Scientific paper

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.

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