Contents

# Contents

## Idea

The concept of Borcherds algebra or Borcherds-Kac-Moody algebra is a generalization of that of Kac-Moody algebra (hence also called generalized Kac-Moody algebra) obtained by allowing imaginary simple roots.

## References

• Richard Borcherds, Generalized Kac-Moody algebras, J. Algebra 115 (1988), 501–512.

• Richard Borcherds, Central extensions of generalized Kac-Moody algebras, J. Algebra.140, 330-335 (1991).

• Victor Kac, Infinite dimensional Lie algebras, third edition, Cambridge University Press, 1990.

Relation to U-duality and E11 (via mysterious duality) is discussed in

and specifically to exceptional generalized geometry in

• Jakob Palmkvist, Exceptional geometry and Borcherds superalgebras (arXiv:1507.08828)

• Jakob Palmkvist, Tensor hierarchies, Borcherds algebras and $E_{11}$, JHEP 1202 (2012) 066 (arXiv:1110.4892)