LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY, I: GRAPH COALGEBRAS

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2011-01-01

Author

Sinha, Dev
Walter, Benjamin

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We give a new presentation of the Lie cooperad as a quotient of the graph cooperad, a presentation which is not linearly dual to any of the standard presentations of the Lie operad. We use this presentation to explicitly compute duality between Lie algebras and coalgebras, to give a new presentation of Harrison homology, and to show that Lyndon words yield a canonical basis for cofree Lie coalgebras.

Subject Keywords

Graph cohomology, Rational homotopy theory, Lie coalgebras

URI

https://hdl.handle.net/11511/65630

Journal

HOMOLOGY HOMOTOPY AND APPLICATIONS

DOI

https://doi.org/10.4310/hha.2011.v13.n2.a16

Collections

Natural Sciences and Mathematics, Article

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Citation Formats

D. Sinha and B. Walter, “LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY, I: GRAPH COALGEBRAS,” HOMOLOGY HOMOTOPY AND APPLICATIONS, pp. 263–292, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65630.