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Embedding Groupoid C∗ -Algebras and ...

Zailai, Ali H.,

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Embedding Groupoid C∗ -Algebras and Certain Bimodules in Groupoid C∗ -Algebras /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Embedding Groupoid C∗ -Algebras and Certain Bimodules in Groupoid C∗ -Algebras // Ali H Zailai.
作者:	Zailai, Ali H.,
面頁冊數:	1 electronic resource (74 pages)
附註:	Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
Contained By:	Dissertations Abstracts International87-01B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32184400
ISBN:	9798286457519

Embedding Groupoid C∗ -Algebras and Certain Bimodules in Groupoid C∗ -Algebras /
Zailai, Ali H.,

Embedding Groupoid C∗ -Algebras and Certain Bimodules in Groupoid C∗ -Algebras /Ali H Zailai. - 1 electronic resource (74 pages)

Source: Dissertations Abstracts International, Volume: 87-01, Section: B.

The following thesis is divided into three main chapters. In Chapter 3, for an etale groupoid G equipped with a fixed Fell line bundle L and an open subgroupoid H of G containing G(0), we show thatC0(G(0)) ⊆ C∗r (H, LH) ⊆ C∗r (G, L).This is an extension of what Brown, Fuller, Pitts, and Reznikoff proved in the Hausdorff setting, [1, Lemma 2.19].Moreover, if G is topologically free, we define the essential groupoid C∗ -algebra C∗ess(G, L) to be the quotient of C∗r (G, L) by the largest ideal of C∗r (G, L) that has trivial intersection with C0(G(0)). We show that C0(G(0)) ⊆ C∗ (H, LH) ⊆ C∗ess(G, L).In Chapter 4, we gave an extension of a theorem due to Kumora. In particular, we study the closed C0(G(0))-bimodules for an etale groupoid G equipped with a fixed Fell line bundle L. If NG is the ∗-subsemigroup of the set of all normalizer of C0(G(0)) within C∗r (G, L) which contains elements of bisection support, and M a closed linear subspace of C∗r (G, L) we show that M is generated by elements from NG if and only if there exist an open set U ⊆ G such thatM = Cc(U, L).In chapter 5 we study the example of a non-Hausdorff, etale, and effective groupoid given by Excel in [4]. Exel presented an example of a normalizer u ∈ C∗r (G) and showed that u is not supported in a bisection and hence not in NG. If u is the normalizer that is not supported in a bisection and M ⊆ C∗r (G) is a closed C0(G(0))-bimodule generated by u, we show that there is not an open set U ⊆ G for whichM = Cc(U)Hence, in a non-Hausdorff setting, even if the groupoid G is effective, our result is not extended to cover the set of all normalizers, and we have to restrict our choice to NG.

English

ISBN: 9798286457519Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Bimodules

Embedding Groupoid C∗ -Algebras and Certain Bimodules in Groupoid C∗ -Algebras /
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500 $a Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
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502 $b Ph.D. $c Ohio University $d 2025.
520 $a The following thesis is divided into three main chapters. In Chapter 3, for an etale groupoid G equipped with a fixed Fell line bundle L and an open subgroupoid H of G containing G(0), we show thatC0(G(0)) ⊆ C∗r (H, LH) ⊆ C∗r (G, L).This is an extension of what Brown, Fuller, Pitts, and Reznikoff proved in the Hausdorff setting, [1, Lemma 2.19].Moreover, if G is topologically free, we define the essential groupoid C∗ -algebra C∗ess(G, L) to be the quotient of C∗r (G, L) by the largest ideal of C∗r (G, L) that has trivial intersection with C0(G(0)). We show that C0(G(0)) ⊆ C∗ (H, LH) ⊆ C∗ess(G, L).In Chapter 4, we gave an extension of a theorem due to Kumora. In particular, we study the closed C0(G(0))-bimodules for an etale groupoid G equipped with a fixed Fell line bundle L. If NG is the ∗-subsemigroup of the set of all normalizer of C0(G(0)) within C∗r (G, L) which contains elements of bisection support, and M a closed linear subspace of C∗r (G, L) we show that M is generated by elements from NG if and only if there exist an open set U ⊆ G such thatM = Cc(U, L).In chapter 5 we study the example of a non-Hausdorff, etale, and effective groupoid given by Excel in [4]. Exel presented an example of a normalizer u ∈ C∗r (G) and showed that u is not supported in a bisection and hence not in NG. If u is the normalizer that is not supported in a bisection and M ⊆ C∗r (G) is a closed C0(G(0))-bimodule generated by u, we show that there is not an open set U ⊆ G for whichM = Cc(U)Hence, in a non-Hausdorff setting, even if the groupoid G is effective, our result is not extended to cover the set of all normalizers, and we have to restrict our choice to NG.
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590 $a School code: 0167
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Bimodules
653 $a Fell line bundle
653 $a Groupoid G
653 $a Subsemigroup
653 $a Non-Hausdorff setting
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690 $a 0364
710 2 $a Ohio University. $b Mathematics (Arts and Sciences). $e degree granting institution. $3 3823238
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