The tensor product of m-partition algebras as a centralizer algebra of
In this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor prod...
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World Scientific Publishing
2025-01-01
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| Series: | Mathematics Open |
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2811007225300010 |
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| author | Amani M. Alfadhli |
| author_facet | Amani M. Alfadhli |
| author_sort | Amani M. Alfadhli |
| collection | DOAJ |
| description | In this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor products [Formula: see text], where [Formula: see text]. In particular, we restrict the action of the direct products of symmetric groups, [Formula: see text], to the action of the direct product of alternating groups, [Formula: see text]. Herein, we determine the basis for the centralizer algebra and exhibit that when the centralizer is isomorphic to the tensor product of m-partition algebras, [Formula: see text]. |
| format | Article |
| id | doaj-art-032d487a5d744c2ebbb97e62f734b04e |
| institution | Kabale University |
| issn | 2811-0072 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Mathematics Open |
| spelling | doaj-art-032d487a5d744c2ebbb97e62f734b04e2025-08-20T03:51:07ZengWorld Scientific PublishingMathematics Open2811-00722025-01-010410.1142/S2811007225300010The tensor product of m-partition algebras as a centralizer algebra ofAmani M. Alfadhli0Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi ArabiaIn this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor products [Formula: see text], where [Formula: see text]. In particular, we restrict the action of the direct products of symmetric groups, [Formula: see text], to the action of the direct product of alternating groups, [Formula: see text]. Herein, we determine the basis for the centralizer algebra and exhibit that when the centralizer is isomorphic to the tensor product of m-partition algebras, [Formula: see text].https://www.worldscientific.com/doi/10.1142/S2811007225300010Centralizer algebraalternating grouppartition algebra |
| spellingShingle | Amani M. Alfadhli The tensor product of m-partition algebras as a centralizer algebra of Mathematics Open Centralizer algebra alternating group partition algebra |
| title | The tensor product of m-partition algebras as a centralizer algebra of |
| title_full | The tensor product of m-partition algebras as a centralizer algebra of |
| title_fullStr | The tensor product of m-partition algebras as a centralizer algebra of |
| title_full_unstemmed | The tensor product of m-partition algebras as a centralizer algebra of |
| title_short | The tensor product of m-partition algebras as a centralizer algebra of |
| title_sort | tensor product of m partition algebras as a centralizer algebra of |
| topic | Centralizer algebra alternating group partition algebra |
| url | https://www.worldscientific.com/doi/10.1142/S2811007225300010 |
| work_keys_str_mv | AT amanimalfadhli thetensorproductofmpartitionalgebrasasacentralizeralgebraof AT amanimalfadhli tensorproductofmpartitionalgebrasasacentralizeralgebraof |