nLab
Borcherds algebra

Contents

Context

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

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 11E_{11}, JHEP 1202 (2012) 066 (arXiv:1110.4892)

See also:

Last revised on September 13, 2019 at 13:36:57. See the history of this page for a list of all contributions to it.