On Hom-$F$-manifold algebras and quantization
Abstract
The notion of a -manifold algebras is an algebraic description of a -manifold. In this paper, we introduce the notion of Hom--manifold algebras which is generalisation of -manifold algebras and Hom-Poisson algebras. We develop the representation theory of Hom--manifold algebras and generalize the notion of Hom-pre-Poisson algebras by introducing the Hom-pre--manifold algebras which give rise to a Hom--manifold algebra through the sub-adjacent commutative Hom-associative algebra and the sub-adjacent Hom-Lie algebra. Using -operators on a Hom--manifold algebras we construct a Hom-pre--manifold algebras on a module. Then, we study Hom-pre-Lie formal deformations of commutative Hom-associative algebra and prove that Hom--manifold algebras are the corresponding semi-classical limits. Finally, we study Hom-Lie infinitesimal deformations and extension of Hom-pre-Lie -deformation to Hom-pre-Lie -deformation of a commutative Hom-associative algebra via cohomology theory.
Keywords
Cite
@article{arxiv.2102.05595,
title = {On Hom-$F$-manifold algebras and quantization},
author = {Abdelkader Ben Hassin and Taoufik Chtioui and Mohamed Ali Maalaoui and Sami Mabrouk},
journal= {arXiv preprint arXiv:2102.05595},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2002.10238 by other authors