L1-DETERMINED PRIMITIVE IDEALS IN THE C∗-ALGEBRA OF AN EXPONENTIAL LIE GROUP WITH CLOSED NON-∗-REGULAR ORBITS
L1-DETERMINED PRIMITIVE IDEALS IN THE C∗-ALGEBRA OF AN EXPONENTIAL LIE GROUP WITH CLOSED NON-∗-REGULAR ORBITS
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闭非正规轨道指数李群C*代数中L1确定的本原理想
DOI：
10.2206/kyushujm.74.127
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发表时间：
2020
影响因子：
0.4
通讯作者：
J. Ludwig
中科院分区：
文献类型：
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作者：
Junko Inoue;J. Ludwig
让G = exp (G)是一个指数可解李集团和广告(G)⊂D指数可解李群同构的G .假定每一个非∗常规轨道D·q q∈G, G D = exp (D),存在一个幂零理想的n G包含D·D·G这样的问| n是封闭在n。然后,我们表明,每D-orbitG内核柯尔克∗()G的C-algebra L1-determined,这意味着柯尔克∗()关闭内核kerL1()的组代数1 L (G)。这也建立了Ungermann对平凡群D= Ad(G)的相同结果的一个新的证明。最后给出了指数可解群G的非闭非∗正则轨道和伴随轨道O∧G的一个例子，它们在C(G)中对应的核kerC∗(πO)不是l1确定的。
Let G = exp(g) be an exponential solvable Lie group and Ad(G)⊂ D an exponential solvable Lie group of automorphisms of G. Assume that for every non-∗-regular orbit D · q, q ∈ g, of D= exp(d) in g, there exists a nilpotent ideal n of g containing d · g such that D · q|n is closed in n. We then show that for every D-orbit in g the kernel kerC∗() of in the C-algebra of G is L1-determined, which means that kerC∗() is the closure of the kernel kerL1() of in the group algebra L 1(G). This establishes also a new proof of a result of Ungermann, who obtained the same result for the trivial group D= Ad(G). We finally give an example of a non-closed non-∗-regular orbit of an exponential solvable group G and of a coadjoint orbit O ⊂ g, for which the corresponding kernel kerC∗(πO) in C(G) is not L1-determined.
DOI：
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发表时间：
2006
期刊：
影响因子：
--
作者：
Takuya Hosokawa;Shuichi Ohno;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara;藤原英徳;Hidenori Fujiwara;H.Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;Hidenori Fujiwara;藤原 英徳;Hidenori Fujiwara
通讯作者：
Hidenori Fujiwara