BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras
A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebra...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2015 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147155 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734347831869440 |
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| author | Graziani, G. Makhlouf, A. Menini, C. Panaite, F. |
| author_facet | Graziani, G. Makhlouf, A. Menini, C. Panaite, F. |
| citation_txt | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc).
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| first_indexed | 2025-12-07T19:42:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147155 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:42:16Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
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| spelling | Graziani, G. Makhlouf, A. Menini, C. Panaite, F. 2019-02-13T17:49:07Z 2019-02-13T17:49:07Z 2015 BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras / G. Graziani, A. Makhlouf, C. Menini, F. Panaite // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17A99; 18D10; 16T99 DOI:10.3842/SIGMA.2015.086 https://nasplib.isofts.kiev.ua/handle/123456789/147155 A BiHom-associative algebra is a (nonassociative) algebra A endowed with two commuting multiplicative linear maps α,β:A→A such that α(a)(bc)=(ab)β(c), for all a,b,c∈A. This concept arose in the study of algebras in so-called group Hom-categories. In this paper, we introduce as well BiHom-Lie algebras (also by using the categorical approach) and BiHom-bialgebras. We discuss these new structures by presenting some basic properties and constructions (representations, twisted tensor products, smash products etc). This paper was written while Claudia Menini was a member of GNSAGA. Florin Panaite was
 supported by a grant of the Romanian National Authority for Scientific Research, CNCSUEFISCDI,
 project number PN-II-ID-PCE-2011-3-0635, contract nr. 253/5.10.2011. Parts of
 this paper have been written while Florin Panaite was a visiting professor at University of Ferrara
 in September 2014, supported by INdAM, and a visiting scholar at the Erwin Schrodinger
 Institute in Vienna in July 2014 in the framework of the “Combinatorics, Geometry and Physics”
 programme; he would like to thank both these institutions for their warm hospitality.
 The authors are grateful to the referees for their remarks and questions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras Article published earlier |
| spellingShingle | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras Graziani, G. Makhlouf, A. Menini, C. Panaite, F. |
| title | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras |
| title_full | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras |
| title_fullStr | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras |
| title_full_unstemmed | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras |
| title_short | BiHom-Associative Algebras, BiHom-Lie Algebras and BiHom-Bialgebras |
| title_sort | bihom-associative algebras, bihom-lie algebras and bihom-bialgebras |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147155 |
| work_keys_str_mv | AT grazianig bihomassociativealgebrasbihomliealgebrasandbihombialgebras AT makhloufa bihomassociativealgebrasbihomliealgebrasandbihombialgebras AT meninic bihomassociativealgebrasbihomliealgebrasandbihombialgebras AT panaitef bihomassociativealgebrasbihomliealgebrasandbihombialgebras |