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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188360 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862569591301996544 |
|---|---|
| author | Karimilla Bi, N. Parvathi, M. |
| author_facet | Karimilla Bi, N. Parvathi, M. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-26T01:45:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188360 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T01:45:40Z |
| publishDate | 2018 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Karimilla Bi, N. Parvathi, M. 2023-02-25T14:47:49Z 2023-02-25T14:47:49Z 2018 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 https://nasplib.isofts.kiev.ua/handle/123456789/188360 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. The authors would like to express their gratitude and sincere thanks to the referee for all his(her) valuable comments and suggestions which in turn made the paper easy to read. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Gram matrices and Stirling numbers of a class of diagram algebras, II Article published earlier |
| spellingShingle | Gram matrices and Stirling numbers of a class of diagram algebras, II Karimilla Bi, N. Parvathi, M. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188360 |
| work_keys_str_mv | AT karimillabin grammatricesandstirlingnumbersofaclassofdiagramalgebrasii AT parvathim grammatricesandstirlingnumbersofaclassofdiagramalgebrasii |