Universal coverings of Steinberg Lie algebras of small characteristic

It is well-known that the second homology group \(H_2(\st)\) of the Steinberg Lie algebra \(\st\) is trivial when \(n\geq 5\). In this paper, we will work out \(H_2(\st)\) explicitly for \(n=3, 4\) which are not necessarily trivial. Consequently, we obtained \(H_2(sl_n(R))\) for \(n=3, 4\).

Saved in:
Bibliographic Details
Published in:arXiv.org 2005-12
Main Authors: Gao, Yun, Shang, Shikui
Format: Article
Language:English
Subjects:
Homology
Lie groups
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is well-known that the second homology group \(H_2(\st)\) of the Steinberg Lie algebra \(\st\) is trivial when \(n\geq 5\). In this paper, we will work out \(H_2(\st)\) explicitly for \(n=3, 4\) which are not necessarily trivial. Consequently, we obtained \(H_2(sl_n(R))\) for \(n=3, 4\).
ISSN:2331-8422