Tensor product of cyclic A$_\infty$-algebras and their Kontsevich classes

Lino Amorim; Junwu Tu

Tensor product of cyclic A$_\infty$-algebras and their Kontsevich classes

Quantum Algebra 2021-04-22 v2 Algebraic Geometry Algebraic Topology

Authors: Lino Amorim , Junwu Tu

Abstract

Given two cyclic A $_\infty$ -algebras $A$ and $B$ , we prove that there exists a cyclic A $_\infty$ -algebra structure on their tensor product $A\otimes B$ which is unique up to a cyclic A $_\infty$ -quasi-isomorphism. Furthermore, the Kontsevich class of $A\otimes B$ is equal to the cup product of the Kontsevich classes of $A$ and $B$ on the moduli space of curves.

Keywords

cyclic A$_\infty$-algebras tensor product Kontsevich class quasi-isomorphism moduli space of curves cup product

Cite

@article{arxiv.1311.4073,
  title  = {Tensor product of cyclic A$_\infty$-algebras and their Kontsevich classes},
  author = {Lino Amorim and Junwu Tu},
  journal= {arXiv preprint arXiv:1311.4073},
  year   = {2021}
}

Comments

v2: One mistake fixed, expanded discussion of odd inner products

Tensor product of cyclic A$_\infty$-algebras and their Kontsevich classes

Abstract

Keywords

Cite

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