Ternary derivations of finite-dimensional real division algebras

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• 作者：Clara Jimé ; nez-Gestal ; José ; M. Pé ; rez-Izquierdo
• 关键词：Real division algebras ; Ternary derivations
• 刊名：Linear Algebra and its Applications
• 出版年：2008
• 出版时间：15 April 2008
• 年：2008
• 卷：428
• 期：8-9
• 页码：2192-2219
• 全文大小：288 K

文摘

We present for each style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4RR86XN-1&_mathId=mml1&_user=10&_cdi=5653&_rdoc=33&_acct=C000050221&_version=1&_userid=10&md5=c0cc5cf253931df1e2434c8bbb900ff3"" title=""Click to view the MathML source"">n{1,2,4,8} a group acting on the set of all division algebra structures on , and an invariant, the Lie algebra of ternary derivations, for this action. An exploration of these structures is conducted in terms of this new invariant obtaining simple descriptions of the division algebras involved. In the course of the investigation another family of algebras is considered, among them the algebra style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4RR86XN-1&_mathId=mml3&_user=10&_cdi=5653&_rdoc=33&_acct=C000050221&_version=1&_userid=10&md5=be67324118c79da34f3dc2a26406e43a"" title=""Click to view the MathML source"">sl(4,F) of style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0R-4RR86XN-1&_mathId=mml4&_user=10&_cdi=5653&_rdoc=33&_acct=C000050221&_version=1&_userid=10&md5=8186d64874783adb20030377b82b447d"" title=""Click to view the MathML source"">4×4 traceless matrices with the symmetric product shows an exceptional behavior.