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Symmetric homology and representation homology.
- Source :
-
Transactions of the American Mathematical Society . Sep2023, Vol. 376 Issue 9, p6475-6496. 22p. - Publication Year :
- 2023
-
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 (1991) and was further developed in the work of S. Ault (2010). In this paper, we show that, for algebras defined over a field of characteristic 0, the symmetric homology is naturally equivalent to the (one-dimensional) representation homology introduced by the authors in joint work with G. Khachatryan (2013). 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 their main conjecture (2007) on topological interpretation of symmetric homology of polynomial algebras. [ABSTRACT FROM AUTHOR]
- Subjects :
- *UNIVERSAL algebra
*LIE algebras
*HOMOLOGY theory
*AUTHORSHIP collaboration
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 376
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 170039166
- Full Text :
- https://doi.org/10.1090/tran/8947