On the algebra generated by $\overline{\mu}, \overline{\partial}, \partial, \mu$
Differential Geometry
2023-05-08 v2 Algebraic Topology
Abstract
In this note, we determine the structure of the associative algebra generated by the differential operators that act on complex-valued differential forms of almost complex manifolds. This is done by showing it is the universal enveloping algebra of the graded Lie algebra generated by these operators and determining the structure of the corresponding graded Lie algebra. We then determine the cohomology of this graded Lie algebra with respect to its canonical inner differential , as well as its cohomology with respect to all its inner differentials.
Cite
@article{arxiv.2208.04890,
title = {On the algebra generated by $\overline{\mu}, \overline{\partial}, \partial, \mu$},
author = {Shamuel Auyeung and Jin-Cheng Guu and Jiahao Hu},
journal= {arXiv preprint arXiv:2208.04890},
year = {2023}
}
Comments
To appear in Complex Manifolds. Minor improvements. 9 pages