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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 \(n=3, 4\).

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Published in:arXiv.org 2005-12
Main Authors: Gao, Yun, Shang, Shikui
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description 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 \(n=3, 4\).
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Lie groups
title Universal coverings of Steinberg Lie algebras of small characteristic
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