Extensions of diffeomorphism and current algebras
Larsson, T. A.
arXiv, 0002016 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-02-07
Classification:  Mathematical Physics 
@article{0002016,
     author = {Larsson, T. A.},
     title = {Extensions of diffeomorphism and current algebras},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0002016}
}

Larsson, T. A. Extensions of diffeomorphism and current algebras. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0002016/