One-parameter deformations of the diassociative and dendriform operads
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866915418899218432 |
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| author | Bremner, Murray R. |
| author_facet | Bremner, Murray R. |
| contents | Livernet and Loday constructed a polarization of the nonsymmetric associative operad A with one operation into a symmetric operad SA with two operations (the Lie bracket and Jordan product), and defined a one-parameter deformation of SA which includes Poisson algebras. We combine this with the dendriform splitting of an associative operation into the sum of two nonassociative operations, and use Koszul duality for quadratic operads, to construct one-parameter deformations of the nonsymmetric dendriform and diassociative operads into the category of symmetric operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1602_06026 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | One-parameter deformations of the diassociative and dendriform operads Bremner, Murray R. Quantum Algebra Rings and Algebras 17A30 (Primary), 15A21, 15A54, 16S80, 17A50, 17B63, 18D50 (Secondary) Livernet and Loday constructed a polarization of the nonsymmetric associative operad A with one operation into a symmetric operad SA with two operations (the Lie bracket and Jordan product), and defined a one-parameter deformation of SA which includes Poisson algebras. We combine this with the dendriform splitting of an associative operation into the sum of two nonassociative operations, and use Koszul duality for quadratic operads, to construct one-parameter deformations of the nonsymmetric dendriform and diassociative operads into the category of symmetric operads. |
| title | One-parameter deformations of the diassociative and dendriform operads |
| topic | Quantum Algebra Rings and Algebras 17A30 (Primary), 15A21, 15A54, 16S80, 17A50, 17B63, 18D50 (Secondary) |
| url | https://arxiv.org/abs/1602.06026 |