Restricted one-dimensional central extensions of restricted simple Lie algebras

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• 作者：Tyler J. Evans^a ; ¹ ; ^{evans@humboldt.edu" class="auth_mail" title="E-mail the corresponding author} ; Alice Fialowski^b ; ^{fialowsk@cs.elte.hu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：17B56 ; 17B50
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：513
• 期：Complete
• 页码：96-102
• 全文大小：267 K

文摘

We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for p≥5$p\ge 5$. For H²(g)=0$H^2(\mathfrak{g})=0$, we explicitly describe the cocycles spanning $H_{⁎}^2(\mathfrak{g})$, and in the case H²(g)≠0$H^2(\mathfrak{g})\ne 0$, we give a procedure to describe a basis for $H_{⁎}^2(\mathfrak{g})$.