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- W4307005942 abstract "Symmetric homology is a natural generalization of cyclic homology, in which symmetric groups play the role of cyclic groups. In the case of associative algebras, the symmetric homology theory was introduced by Z. Fiedorowicz cite{F} and was further developed in the work of S. Ault cite{Au1, Au2}. In this paper, we show that, for algebras defined over a field of characteristic $0$, the symmetric homology theory is naturally equivalent to the (one-dimensional) representation homology theory introduced by the authors (jointly with G. Khachatryan) in cite{BKR}. Using known results on representation homology, we compute symmetric homology explicitly for basic algebras, such as polynomial algebras and universal enveloping algebras of (DG) Lie algebras. As an application, we prove two conjectures of Ault and Fiedorowicz, including the main conjecture of cite{AF07} on topological interpretation of symmetric homology of polynomial algebras." @default.
- W4307005942 created "2022-10-22" @default.
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- W4307005942 date "2022-10-18" @default.
- W4307005942 modified "2023-09-27" @default.
- W4307005942 title "Symmetric Homology is Representation Homology" @default.
- W4307005942 doi "https://doi.org/10.48550/arxiv.2210.10131" @default.
- W4307005942 hasPublicationYear "2022" @default.
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