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| Main Author: | |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1802.08171 |
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| _version_ | 1866912374644015104 |
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| author | Foissy, Loïc |
| author_facet | Foissy, Loïc |
| contents | A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and coproduct. We here give a classification of connected, cocommutative Com-PreLie bialgebras over a field of characteristic zero: we obtain a main family of symmetric algebras on a space V of any dimension, and another family available only if V is one-dimensional. We also explore the case of Com-PreLie bialgebras over a group algebra and over a tensor product of a group algebra and of a symmetric algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1802_08171 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Cocommutative Com-PreLie bialgebras Foissy, Loïc Rings and Algebras A Com-PreLie bialgebra is a commutative bialgebra with an extra preLie product satisfying some compatibilities with the product and coproduct. We here give a classification of connected, cocommutative Com-PreLie bialgebras over a field of characteristic zero: we obtain a main family of symmetric algebras on a space V of any dimension, and another family available only if V is one-dimensional. We also explore the case of Com-PreLie bialgebras over a group algebra and over a tensor product of a group algebra and of a symmetric algebra. |
| title | Cocommutative Com-PreLie bialgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/1802.08171 |