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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Lugansk National Taras Shevchenko University
2018
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-07-24T22:56:15Z |
| collection |
OJS |
| language |
English |
| topic |
Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 |
| 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 |
| topic_facet |
Gram matrices partition algebras signed partition algebras and the algebra of \(\mathbb{Z}_2\)-relations 16Z05 |
| format |
Article |
| author |
Karimilla Bi, N. Parvathi, M. |
| author_facet |
Karimilla Bi, N. Parvathi, M. |
| author_sort |
Karimilla Bi, N. |
| title |
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_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_sort |
gram matrices and stirling numbers of a class of diagram algebras, ii |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1219 |
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AT karimillabin grammatricesandstirlingnumbersofaclassofdiagramalgebrasii AT parvathim grammatricesandstirlingnumbersofaclassofdiagramalgebrasii |
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2025-07-17T10:34:14Z |
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2025-07-17T10:34:14Z |
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1837889964404113408 |