Abstract Hodge decomposition and minimal models for cyclic algebras

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy.

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Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Chuang, Joseph, Lazarev, Andrey
Format: Article
Language:English
Subjects:
Decomposition
Linear algebra
Online Access:Get full text
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Description
Summary:We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy.
ISSN:2331-8422
DOI:10.48550/arxiv.0810.2393