# Bosonic and fermionic representations of Lie algebra central extensions

@article{Lau2004BosonicAF,
title={Bosonic and fermionic representations of Lie algebra central extensions},
author={Michael Lau},
year={2004},
volume={194},
pages={225-245}
}
• Michael Lau
• Published 29 May 2004
• Mathematics

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## References

SHOWING 1-10 OF 22 REFERENCES

### Bosonic and fermionic realizations of the affine algebra $$g\hat l_n$$

• Mathematics
• 1991
AbstractWe give an explicit description of all inequivalent Heisenberg subalgebras of the affine Lie algebra $$g\hat l_n (\mathbb{C})$$ and the associated vertex operator constructions of the level

### Bosonic and Fermionic Realizations of The Affine Algebra sˆo2n

• Mathematics
• 1992
We give an explicit description of the Kac-Peterson-Lepowsky constr tion of the basic representation for the affine Lie algebra sˆo2n(C). Using the conjugacy classes of the Weyl group of sˆo2n(C), we

### Spin and wedge representations of infinite-dimensional Lie algebras and groups.

• Mathematics
Proceedings of the National Academy of Sciences of the United States of America
• 1981
A construction of all level-one highest-weight representations of orthogonal affine Lie algebras in terms of creation and annihilation operators on an infinite-dimensional Grassmann algebra is deduced.

### Infinite additional symmetries in two-dimensional conformal quantum field theory

This paper investigates additional symmetries in two-dimensional conformal field theory generated by spin s = 1/2, 1,...,3 currents. For spins s = 5/2 and s = 3, the generators of the symmetry form

### Lie Algebras with Triangular Decompositions

• Mathematics
• 1995
Lie Algebras. Lie Algebras Admitting Triangular Decompositions. Lattices and Root Systems. Contragredient Lie Algebras. The Weyl Group and Its Geometry. Category O for Kac--Moody Algebras. Conjugacy

### Representation Theory: A First Course

• Mathematics
• 1991
This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation