F-manifold algebras and deformation quantization via pre-Lie algebras
F-manifold algebras and deformation quantization via pre-Lie algebras
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F-流形代数和通过前李代数的变形量化
DOI：
10.1016/j.jalgebra.2020.04.029
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发表时间：
2020-02
影响因子：
0.9
通讯作者：
Chengming Bai
中科院分区：
文献类型：
--
作者：
Jiefeng Liu;Yunhe Sheng;Chengming Bai
The notion of an F-manifold algebra is the underlying algebraic structure of an F-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding semi-classical limits. We study pre-Lie infinitesimal deformations and extension of pre-Lie n-deformation to pre-Lie (n+ 1)-deformation of a commutative associative algebra through the cohomology groups of pre-Lie algebras. We introduce the notions of pre-F-manifold algebras and dual pre-F-manifold algebras, and show that a pre-F-manifold algebra gives rise to an F-manifold algebra through the sub-adjacent associative algebra and the sub-adjacent Lie algebra. We use Rota-Baxter operators, more generally O-operators and average operators on F-manifold algebras to construct pre-F-manifold algebras and dual pre-F-manifold algebras.
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影响因子：
0.4
作者：
I. Gel'fand;I. Dorfman
通讯作者：
I. Gel'fand;I. Dorfman
DOI：
10.1093/imrn/rnv362
发表时间：
2013-07
期刊：
arXiv: Quantum Algebra
影响因子：
--
作者：
R. Bandiera
通讯作者：
R. Bandiera
影响因子：
--
作者：
D. Burde
通讯作者：
D. Burde
DOI：
10.1017/cbo9780511543104
发表时间：
2002
期刊：
--
影响因子：
--
作者：
C. Hertling
通讯作者：
C. Hertling
DOI：
10.17323/1609-4514-2016-16-3-505-543
发表时间：
2015-02
期刊：
arXiv: Quantum Algebra
影响因子：
--
作者：
V. Dotsenko;S. Shadrin;B. Vallette
通讯作者：
V. Dotsenko;S. Shadrin;B. Vallette