On the Symmetric Homology of Algebras

On the Symmetric Homology of Algebras

Bibliographic Details
Main Author: Ault, Shaun V.
Language:English
Published: The Ohio State University / OhioLINK 2008
Subjects:
Mathematics
Symmetric Homology
Functor Homology
Crossed Simplicial Groups
Chessboard Complexes
Homology Operations
GAP
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
id ndltd-OhioLink-oai-etd.ohiolink.edu-osu1218237992
record_format oai_dc
spelling ndltd-OhioLink-oai-etd.ohiolink.edu-osu12182379922021-08-03T05:54:20Z On the Symmetric Homology of Algebras Ault, Shaun V. Mathematics Symmetric Homology Functor Homology Crossed Simplicial Groups Chessboard Complexes Homology Operations GAP Symmetric homology is an analog of cyclic homology in which the cyclic groups are replaced by symmetric groups. The foundations for the theory of symmetric homology of algebras are developed in the context of crossed simplicial groups using derived functors and the symmetric bar construction of Fiedorowicz. The symmetric homology of group rings is related to stable homotopy theory. Two chain complexes are constructed that compute symmetric homology, as well as two spectral sequences. In the setup of the second spectral sequence, a complex isomorphic to the suspension of the cycle-free chessboard complex of Vrecica and Zivaljevic appears. Homology operations are defined on the symmetric homology groups over Z/p, p a prime. Finally, an explicit partial resolution is presented, permitting the computation of the zeroth and first symmetric homology groups of finite-dimensional algebras. 2008-09-11 English text The Ohio State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992 http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Symmetric Homology
Functor Homology
Crossed Simplicial Groups
Chessboard Complexes
Homology Operations
GAP
spellingShingle Mathematics
Symmetric Homology
Functor Homology
Crossed Simplicial Groups
Chessboard Complexes
Homology Operations
GAP
Ault, Shaun V.
On the Symmetric Homology of Algebras
author Ault, Shaun V.
author_facet Ault, Shaun V.
author_sort Ault, Shaun V.
title On the Symmetric Homology of Algebras
title_short On the Symmetric Homology of Algebras
title_full On the Symmetric Homology of Algebras
title_fullStr On the Symmetric Homology of Algebras
title_full_unstemmed On the Symmetric Homology of Algebras
title_sort on the symmetric homology of algebras
publisher The Ohio State University / OhioLINK
publishDate 2008
url http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
work_keys_str_mv AT aultshaunv onthesymmetrichomologyofalgebras
_version_ 1719427493129093120

Similar Items