Integrable module

This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.
Find sources: "Integrable module" – news · newspapers · books · scholar · JSTOR (May 2024)

In algebra, an integrable module (or integrable representation) of a Kac–Moody algebra ${\mathfrak {g}}$ (a certain infinite-dimensional Lie algebra) is a representation of ${\mathfrak {g}}$ such that (1) it is a sum of weight spaces and (2) the Chevalley generators $e_{i},f_{i}$ of ${\mathfrak {g}}$ are locally nilpotent.^[1] For example, the adjoint representation of a Kac–Moody algebra is integrable.^[2]

Notes

^ Kac 1990, § 3.6.
^ Kac 1990, Lemma 3.5.

References

Kac, Victor (1990). Infinite dimensional Lie algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8.

This algebra-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.