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osu1218237992.pdf (826.7 KB)
ETD Abstract Container
Abstract Header
On the Symmetric Homology of Algebras
Author Info
Ault, Shaun V.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
Abstract Details
Year and Degree
2008, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Zbigniew Fiedorowicz (Advisor)
Dan Burghelea (Committee Member)
Roy Joshua (Committee Member)
Avi Benatar (Committee Member)
Pages
166 p.
Subject Headings
Mathematics
Keywords
Symmetric Homology
;
Functor Homology
;
Crossed Simplicial Groups
;
Chessboard Complexes
;
Homology Operations
;
GAP
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Citations
Ault, S. V. (2008).
On the Symmetric Homology of Algebras
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
APA Style (7th edition)
Ault, Shaun.
On the Symmetric Homology of Algebras.
2008. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992.
MLA Style (8th edition)
Ault, Shaun. "On the Symmetric Homology of Algebras." Doctoral dissertation, Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1218237992
Chicago Manual of Style (17th edition)
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Document number:
osu1218237992
Download Count:
825
Copyright Info
© 2008, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.