Tensor product of filtered \(A_\infty\)-algebras. (English) Zbl 1344.18012
The author defines the tensor product of filtered \(A_\infty\)-algebras, establishes some of its properties and gives a partial description of the space of bounding cochains in the tensor product. In the case of classical \(A_\infty\)-algebras, the definition recovers the one given by M. Markl and S. Shnider [Trans. Am. Math. Soc. 358, No. 6, 2353–2372 (2006; Zbl 1093.18005)]. The author also gives a criterion that implies that a given \(A_\infty\)-algebra is quasi-isomorphic to the tensor product of two subalgebras.
Reviewer: Philippe Gaucher (Paris)
MSC:
| 18G55 | Nonabelian homotopical algebra (MSC2010) |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
Citations:
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