Dendriform Algebras Relative to a Semigroup
Loday's dendriform algebras and their siblings, pre-Lie and zinbiel, have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each operation is replaced by a family of operations indexed by a fixed se...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210782 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Dendriform Algebras Relative to a Semigroup. Marcelo Aguiar. SIGMA 16 (2020), 066, 15 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862533144493686784 |
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| author | Aguiar, Marcelo |
| author_facet | Aguiar, Marcelo |
| citation_txt | Dendriform Algebras Relative to a Semigroup. Marcelo Aguiar. SIGMA 16 (2020), 066, 15 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Loday's dendriform algebras and their siblings, pre-Lie and zinbiel, have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each operation is replaced by a family of operations indexed by a fixed semigroup . The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra, but in reference to the monoidal category of -graded vector spaces.
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| first_indexed | 2026-03-12T14:20:30Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-210782 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-12T14:20:30Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
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| spelling | Aguiar, Marcelo 2025-12-17T14:38:08Z 2020 Dendriform Algebras Relative to a Semigroup. Marcelo Aguiar. SIGMA 16 (2020), 066, 15 pages 1815-0659 2020 Mathematics Subject Classification: 17A30; 18C40; 18M05 arXiv:2003.11127 https://nasplib.isofts.kiev.ua/handle/123456789/210782 https://doi.org/10.3842/SIGMA.2020.066 Loday's dendriform algebras and their siblings, pre-Lie and zinbiel, have received attention over the past two decades. In recent literature, there has been interest in a generalization of these types of algebra in which each operation is replaced by a family of operations indexed by a fixed semigroup . The purpose of this note is twofold. First, we add to the existing work by showing that a similar extension is already for the most familiar types of algebra: commutative, associative, and Lie. Second, we show that these concepts arise naturally and in a unified manner from a categorical perspective. For this, one simply has to consider the standard types of algebra, but in reference to the monoidal category of -graded vector spaces. The author thanks the referees for pertinent comments and suggestions. Research partially supported by Simons grant 560656. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Dendriform Algebras Relative to a Semigroup Article published earlier |
| spellingShingle | Dendriform Algebras Relative to a Semigroup Aguiar, Marcelo |
| title | Dendriform Algebras Relative to a Semigroup |
| title_full | Dendriform Algebras Relative to a Semigroup |
| title_fullStr | Dendriform Algebras Relative to a Semigroup |
| title_full_unstemmed | Dendriform Algebras Relative to a Semigroup |
| title_short | Dendriform Algebras Relative to a Semigroup |
| title_sort | dendriform algebras relative to a semigroup |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210782 |
| work_keys_str_mv | AT aguiarmarcelo dendriformalgebrasrelativetoasemigroup |