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See detailThe low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in natural modules
Ecker, Jill Marie-Anne UL; Schlichenmaier, Martin UL

in Banach Center Publications (2020)

The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes ... [more ▼]

The main aim of this contribution is to compute the low-dimensional algebraic cohomology of the Witt and the Virasoro algebra with values in the adjoint and the trivial module. The last section includes results for the general tensor densities modules, presented without proof. One of our main results is that the third algebraic cohomology of the Witt algebra with values in the adjoint module vanishes, while it is one-dimensional for the Virasoro algebra. The first and the second algebraic cohomology of the Witt and the Virasoro algebra with values in tensor densities modules vanish for almost all modules. In the case they do not vanish, we give explicit expressions for the generating cocycles. In our work, we consider algebraic cohomology and not only the sub-complex of continuous cohomology, meaning we do not put any continuity constraints on the cochains. Consequently, our results are independent of any choice of an underlying topology, and valid for any concrete realizations of the considered Lie algebras. [less ▲]

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See detailThe low-dimensional algebraic cohomology of the Witt and the Virasoro algebra
Ecker, Jill Marie-Anne UL; Schlichenmaier, Martin UL

in Journal of Physics. Conference Series (2018)

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See detailThe Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra
Ecker, Jill Marie-Anne UL; Schlichenmaier, Martin UL

E-print/Working paper (2017)

A proof of the vanishing of the first and the third cohomology groups of the Witt algebra with values in the adjoint module is given. The proofs given in the present article are completely algebraic and ... [more ▼]

A proof of the vanishing of the first and the third cohomology groups of the Witt algebra with values in the adjoint module is given. The proofs given in the present article are completely algebraic and independent of any underlying topology. They are a generalization of the ones provided by Schlichenmaier, who proved the vanishing of the second cohomology group using purely algebraic methods. In the case of the third cohomology group though, extra difficulties arise and the involved proofs are distinctly more complicated. [less ▲]

Detailed reference viewed: 107 (15 UL)