Factorizable Lie conformal bialgebras, quadratic Rota-Baxter Lie conformal algebras and some induced structures
Abstract
We introduce the notion of factorizable Lie conformal bialgebras and establish their correspondence with quadratic Rota-Baxter Lie conformal algebras of nonzero weight. Consequently, on the one hand, a Lie conformal bialgebra with a Rota-Baxter operator of nonzero weight gives a factorizable Lie conformal bialgebra. And on the other hand, as the conformal analogue of the fact that a quadratic Rota-Baxter Lie algebra induces a generalized pseudo-Hessian post-Lie algebra and a special partial-pre-post-Lie algebra, a quadratic Rota-Baxter Lie conformal algebra as well as a factorizable Lie conformal bialgebra induces a generalized pseudo-Hessian post-Lie conformal algebra and a special partial-pre-post-Lie conformal algebra. Furthermore, we generalize the correspondence between Gel'fand-Dorfman bialgebras and a class of Lie conformal bialgebras to the factorizable cases. There is not only a correspondence between factorizable Gel'fand-Dorfman bialgebras and a class of factorizable Lie conformal bialgebras, but also a correspondence for their corresponding quadratic Rota-Baxter counterparts as well as some induced structures. In particular, there is a construction of factorizable Lie conformal bialgebras from Gel'fand-Dorfman bialgebras with a Rota-Baxter operator of nonzero weight.
Related
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BibTeX
@misc{xu2026factorizable,
title = {{Factorizable Lie conformal bialgebras, quadratic Rota-Baxter Lie conformal algebras and some induced structures}},
author = {Zhongyin Xu and Chengming Bai and Yanyong Hong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28011},
eprint = {2609.28011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Factorizable Lie conformal bialgebras, quadratic Rota-Baxter Lie conformal algebras and some induced structures
AU - Zhongyin Xu
AU - Chengming Bai
AU - Yanyong Hong
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28011
UR - https://arxiv.org/abs/2609.28011
AB - We introduce the notion of factorizable Lie conformal bialgebras and establish their correspondence with quadratic Rota-Baxter Lie conformal algebras of nonzero weight. Consequently, on the one hand, a Lie conformal bialgebra with a Rota-Baxter operator of nonzero weight gives a factorizable Lie conformal bialgebra. And on the other hand, as the conformal analogue of the fact that a quadratic Rota-Baxter Lie algebra induces a generalized pseudo-Hessian post-Lie algebra and a special partial-pre-post-Lie algebra, a quadratic Rota-Baxter Lie conformal algebra as well as a factorizable Lie conformal bialgebra induces a generalized pseudo-Hessian post-Lie conformal algebra and a special partial-pre-post-Lie conformal algebra. Furthermore, we generalize the correspondence between Gel'fand-Dorfman bialgebras and a class of Lie conformal bialgebras to the factorizable cases. There is not only a correspondence between factorizable Gel'fand-Dorfman bialgebras and a class of factorizable Lie conformal bialgebras, but also a correspondence for their corresponding quadratic Rota-Baxter counterparts as well as some induced structures. In particular, there is a construction of factorizable Lie conformal bialgebras from Gel'fand-Dorfman bialgebras with a Rota-Baxter operator of nonzero weight.
ER -