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Semi-infinite cohomology and superconformal algebras

Elena Poletaeva (2001)

Annales de l’institut Fourier

We describe representations of certain superconformal algebras in the semi-infinite Weil complex related to the loop algebra of a complex finite-dimensional Lie algebra and in the semi-infinite cohomology. We show that in the case where the Lie algebra is endowed with a non-degenerate invariant symmetric bilinear form, the relative semi-infinite cohomology of the loop algebra has a structure, which is analogous to the classical structure of the de Rham cohomology in Kähler...

Super boson-fermion correspondence

Victor G. Kac, J. W. Van de Leur (1987)

Annales de l'institut Fourier

We establish a super boson-fermion correspondence, generalizing the classical boson-fermion correspondence in 2-dimensional quantum field theory. A new feature of the theory is the essential non-commutativity of bosonic fields. The superbosonic fields obtained by the super bosonization procedure from super fermionic fields form the affine superalgebra g ˜ l 1 | 1 . The converse, super fermionization procedure, requires introduction of the super vertex operators. As applications, we give vertex operator constructions...

Sur certaines algèbres de Lie de dérivations

Yves Félix, Stephen Halperin, Jean-Claude Thomas (1982)

Annales de l'institut Fourier

Il est démontré que toute a.d.g.c. ayant un modèle minimal de Sullivan de type fini peut être représentée par une certaine algèbre de Lie différentielle graduée de dérivations. En particulier on peut ainsi représenter le type d’homotopie rationnelle d’un espace topologique.

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