Gram matrices and Stirling numbers of a class of diagram algebras, II
In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we pr...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1219 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543027850379264 |
|---|---|
| author | Karimilla Bi, N. Parvathi, M. |
| author_facet | Karimilla Bi, N. Parvathi, M. |
| author_sort | Karimilla Bi, N. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-07-24T22:56:15Z |
| description | In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we prove that the Gram matrix is similar to a matrix which is a direct sum of block submatrices. As a consequence, the semisimplicity of a signed partition algebra is established. |
| first_indexed | 2025-12-02T15:38:37Z |
| format | Article |
| id | admjournalluguniveduua-article-1219 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:38:37Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-12192018-07-24T22:56:15Z Gram matrices and Stirling numbers of a class of diagram algebras, II Karimilla Bi, N. Parvathi, M. Gram matrices, partition algebras, signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of \(\mathbb{Z}_2\)-relations and the partition algebras. \((s_1, s_2, r_1, r_2, p_1, p_2)\)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we prove that the Gram matrix is similar to a matrix which is a direct sum of block submatrices. As a consequence, the semisimplicity of a signed partition algebra is established. Lugansk National Taras Shevchenko University 2018-07-25 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1219 Algebra and Discrete Mathematics; Vol 25, No 2 (2018) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1219/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 Karimilla Bi, N. Parvathi, M. Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title | Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title_full | Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title_fullStr | Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title_full_unstemmed | Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title_short | Gram matrices and Stirling numbers of a class of diagram algebras, II |
| title_sort | gram matrices and stirling numbers of a class of diagram algebras, ii |
| topic | Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 |
| topic_facet | Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1219 |
| work_keys_str_mv | AT karimillabin grammatricesandstirlingnumbersofaclassofdiagramalgebrasii AT parvathim grammatricesandstirlingnumbersofaclassofdiagramalgebrasii |