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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn041, 35 pages, doi:10.1093/imrn/rnn041 published on April 25, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Strong homotopy inner product of an A{infty}-algebra

Cheol-Hyun Cho

Department of Mathematical Sciences, Seoul National University, San 56-1, Shinrimdong, Gwanak-gu, Seoul, South Korea

Correspondence: Correspondence to be sent to: chocheol{at}snu.ac.kr

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A{infty}-algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the notion of a nonconstant symplectic structure on the corresponding formal noncommutative supermanifold. We show that (open Gromov–Witten type) potential for a cyclic filtered A{infty}-algebra is invariant under the cyclic filtered A{infty}-homomorphism up to reparameterization, cyclization, and a constant addition, generalizing the work of Kajiura.


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