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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 Z₂-relations and the partition algebras. (s₁, s₂, r₁, r₂, p₁, p₂)-Stirling numbers of the second kind are also introduced and their identities are established. In this paper, we prove that the Gram matrix...
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Інститут прикладної математики і механіки НАН України
2018
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/188360 |
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irk-123456789-1883602023-02-26T01:26:54Z Gram matrices and Stirling numbers of a class of diagram algebras, II Karimilla Bi, N. Parvathi, M. In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of Z₂-relations and the partition algebras. (s₁, s₂, r₁, r₂, p₁, p₂)-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. 2018 Article Gram matrices and Stirling numbers of a class of diagram algebras, II / N. Karimilla Bi, M. Parvathi // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 2. — С. 215–256. — Бібліогр.: 18 назв. — англ. 1726-3255 2010 MSC: 16Z05 http://dspace.nbuv.gov.ua/handle/123456789/188360 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
In the paper [6], we introduced Gram matrices for the signed partition algebras, the algebra of Z₂-relations and the partition algebras. (s₁, s₂, r₁, r₂, p₁, p₂)-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. |
| format |
Article |
| author |
Karimilla Bi, N. Parvathi, M. |
| spellingShingle |
Karimilla Bi, N. Parvathi, M. Gram matrices and Stirling numbers of a class of diagram algebras, II Algebra and Discrete Mathematics |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2018 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188360 |
| citation_txt |
Gram matrices and Stirling numbers of a class of diagram algebras, II / N. Karimilla Bi, M. Parvathi // Algebra and Discrete Mathematics. — 2018. — Vol. 25, № 2. — С. 215–256. — Бібліогр.: 18 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT karimillabin grammatricesandstirlingnumbersofaclassofdiagramalgebrasii AT parvathim grammatricesandstirlingnumbersofaclassofdiagramalgebrasii |
| first_indexed |
2023-10-18T23:08:11Z |
| last_indexed |
2023-10-18T23:08:11Z |
| _version_ |
1796157341291249664 |