Symmetric Homology of Algebras: Foundations
Year: 2009
Type: preprint
Abstract: . Symmetric homology of a unital algebra A over a commutative ground ring k is defined using derived functors and the symmetric bar construction of Fiedorowicz. If A = k[G] is a group ring, then HS∗(k[G]) is related to stable homotopy theory. Two chain complexes that compute HS∗(A) are constructed, both making use of a symmetric monoidal category ∆S+ containing ∆S. Two spectral sequences are found that aid in computing symmetric homology. In the second spectral sequence, a complex isomorphic to the suspension of the cycle-free chessboard complex Ωp+1 of Vrećica and ˇ Zivaljević plays an important role. Recent results on the connectivity of Ωn imply finite-dimensionality of the symmetric homology groups of finite-dimensional algebras.
Source: arXiv (Cornell University)
Author: Shaun V. Ault
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W203885723