On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces
In this paper, we study the notion of approximate biprojectivity and left φ-biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L1K implies that K is compact. Moreover, we investigate left φ-biprojectivity of certa...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4939971 |
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| author | Amir Sahami Mehdi Rostami Seyedeh Fatemeh Shariati Salman Babayi |
| author_facet | Amir Sahami Mehdi Rostami Seyedeh Fatemeh Shariati Salman Babayi |
| author_sort | Amir Sahami |
| collection | DOAJ |
| description | In this paper, we study the notion of approximate biprojectivity and left φ-biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L1K implies that K is compact. Moreover, we investigate left φ-biprojectivity of certain hypergroup algebras, namely, abstract Segal algebras. As a main result, we conclude that (with some mild conditions) the abstract Segal algebra B is left φ-biprojective if and only if K is compact, where K is a hypergroup. We also study the approximate biflatness and left φ-biflatness of hypergroup algebras in terms of amenability of their related hypergroups. |
| format | Article |
| id | doaj-art-5a02c71d066c4dd1bb8619d700e2380d |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5a02c71d066c4dd1bb8619d700e2380d2025-02-03T01:10:37ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4939971On Some Homological Properties of Hypergroup Algebras with Relation to Their Character SpacesAmir Sahami0Mehdi Rostami1Seyedeh Fatemeh Shariati2Salman Babayi3Department of Mathematics Faculty of Basic ScienceDepartment of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceDepartment of MathematicsIn this paper, we study the notion of approximate biprojectivity and left φ-biprojectivity of some Banach algebras, where φ is a character. Indeed, we show that approximate biprojectivity of the hypergroup algebra L1K implies that K is compact. Moreover, we investigate left φ-biprojectivity of certain hypergroup algebras, namely, abstract Segal algebras. As a main result, we conclude that (with some mild conditions) the abstract Segal algebra B is left φ-biprojective if and only if K is compact, where K is a hypergroup. We also study the approximate biflatness and left φ-biflatness of hypergroup algebras in terms of amenability of their related hypergroups.http://dx.doi.org/10.1155/2022/4939971 |
| spellingShingle | Amir Sahami Mehdi Rostami Seyedeh Fatemeh Shariati Salman Babayi On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces Journal of Mathematics |
| title | On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces |
| title_full | On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces |
| title_fullStr | On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces |
| title_full_unstemmed | On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces |
| title_short | On Some Homological Properties of Hypergroup Algebras with Relation to Their Character Spaces |
| title_sort | on some homological properties of hypergroup algebras with relation to their character spaces |
| url | http://dx.doi.org/10.1155/2022/4939971 |
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