多項式環の累次ホッホシルト・ホモロジーと累次サイクリック・ホモロジー

URI http://repository.tsuyama-ct.ac.jp/metadata/80
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Title
多項式環の累次ホッホシルト・ホモロジーと累次サイクリック・ホモロジー
Title Alternative
Iterated Hochschild Homology and Iterated Cyclic Homology of Polynomial Algebra
Author
著者 横谷 正明
著者(別表記) Yokotani Masaaki
Abstract

A minimal Sullivan model for the odd dimensional sphere S(2n-1) is given by the differential graded algebra Λ(α) together with the trivial differential, where |α|=2n-1. Since |α| is odd, Λ(α) is the exterior algebra generated by a single element α. The author determined the iterated Hochshild homology HH{l}*(Λ(α),0) and the iterated cyclic homology HC{l}*(Λ(α),0) of the complex (Λ(α),0) for the iteration degree l=1,2. Let K be an arbitrary field of characteristic zero. In this paper, where the case |α|=2n, that is, the complex is the polynomial algebra K[α] over K, we compute the homologies HH{l}*(K(α),0) and HC{l}*(K(α),0). The complex (K(α),0) is a minimal Sullivan model for the infinitely dimensional complex projective space or the classifying space CP∞=BU(1) for |α|=2, and the classifying space BSU(2)=BSp(1) for |α|=4. Therefore we can obtain the explicit forms of the cohmologies H*(map(T(l),X);K) and H*(E(T)×(T)map(T(l),X);K) of the mapping space map(T(l),X) and the Borel construction E(T)×(T)map(T(l),X) for X=CP∞=BU(1), BSU(2)=BSp(1), where T is the circle and T(l)is the l-dimensinal torus.

Subject
410 Mathematics
Keyword
iterated Hochshild homology
iterated cyclic homology
Publish Date
2006-02-28
Publication Title
津山工業高等専門学校紀要
Publication Title Alternative
Bulletion of Tsuyama National College of Technology
Volume
47
Start Page
137
End Page
143
ISSN
0287-7066
NCID
AN00149351
Publisher
津山工業高等専門学校
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Contents Type
Departmental Bulletin Paper
language
Japanese
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publisher