On C^⁎-algebras of exponential solvable Lie groups and their real ranks

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• 作者：Ingrid Beltiţă ; ^{ingrid.beltita@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{Ingrid.Beltita@imar.ro" class="auth_mail" title="E-mail the corresponding author} ; Daniel Beltiţă ^{beltita@gmail.com" class="auth_mail" title="E-mail the corresponding author Daniel.Beltita@imar.ro" class="auth_mail" title="E-mail the corresponding author}
• 关键词：C⁎C⁎-algebra ; Exponential Lie group ; Real rank ; Stable rank
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：51-58
• 全文大小：314 K

文摘

For any solvable Lie group whose exponential map exp_G⁡:g→G${\exp }_G:\mathfrak{g}\to G$ is bijective, we prove that the real rank of 986283105718bd04e3" title="Click to view the MathML source">C^⁎(G)$C^{⁎}(G)$ is equal to dim⁡(g/[g,g])$\dim (\mathfrak{g}/[\mathfrak{g},\mathfrak{g}])$. We also indicate a proof of a similar formula for the stable rank of 986283105718bd04e3" title="Click to view the MathML source">C^⁎(G)$C^{⁎}(G)$, as well as some estimates on the ideal generated by the projections in 986283105718bd04e3" title="Click to view the MathML source">C^⁎(G)$C^{⁎}(G)$.