# Extended super-Kač-Moody algebras and their super-derivation algebras

@article{Coquereaux1990ExtendedSA, title={Extended super-Ka{\vc}-Moody algebras and their super-derivation algebras}, author={Robert Coquereaux and Luc Frappat and Eric Ragoucy and P. Sorba}, journal={Communications in Mathematical Physics}, year={1990}, volume={133}, pages={1-35} }

We study theN-extended super-Kač-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleAN. The extensions are characterized by 2-cocycles which are computed in terms of the cyclic cohomology of the Grassmann algebra withN generators. The graded algebra of super-derivations compatible with each extension is determined. The casesN=1,2,3 are examined in detail and their relation with the Ademollo et al. superconformal algebras is discussed. We examine the…

## 9 Citations

Double extensions of Lie algebras of Kac-Moody type and applications to some hamiltonian systems

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- 2013

We describe some Lie algebras of the Kac-Moody type, construct their double extensions, central and by derivations; we also construct the corresponding Lie groups in some cases. We study the case of…

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Construction ofN = 2 superconformal algebra from affine algebras with extended symmetry: I

- Mathematics, Physics
- 1995

The purpose of this Letter is to use the idea of the Sugawara-Kač-Todorov construction of theN = 0 andN = 1 superconformal algebras to construct a very simple free-field realization of theN = 2…

Hochschild ( co ) homology of exterior algebras 1

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- 2005

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic…

Hochschild (Co)homology of Exterior Algebras

- Mathematics
- 2005

The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic…

Von Neumann Algebras and Quantum Field Theory

- Mathematics
- 1995

Von Neumann algebras were originally designed as a framework for various subjects, a major motivation coming from quantum theory. Although von Nuemann algebras have since turned out to have…

Berezin integration over anticommuting variables and cyclic cohomology

- Mathematics
- 2004

Berezin integration over fermionic degrees of freedom as a standard tool of quantum field theory is analysed from the viewpoint of noncommutative geometry. It is shown that among the variety of…

An attempt to relate area-preserving diffeomorphisms to Kac-Moody algebras

- Mathematics
- 1991

In the same way as the Virasoro algebra can be connected with Kac-Moody algebras defined on the S1 circle, the area-preserving diffeomorphism algebra SDiff(ℳ), where ℳ is a two-dimensional surface,…

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