|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'503'724
Articles rated: 2609
23 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Topological Hochschild cohomology and generalized Morita equivalence | | Andrew Baker
; Andrey Lazarev
; | | Date: |
31 Aug 2002 | | Journal: | Algebr. Geom. Topol. 4 (2004) 623-645 | | Subject: | Algebraic Topology MSC-class: 16E40, 18G60, 55P43, 18G15, 55U99 | math.AT | | Abstract: | We explore two constructions in homotopy category with algebraic precursors in the theory of noncommutative rings and homological algebra, namely the Hochschild cohomology of ring spectra and Morita theory. The present paper provides an extension of the algebraic theory to include the case when $M$ is not necessarily a progenerator. Our approach is complementary to recent work of Dwyer and Greenlees and of Schwede and Shipley. A central notion of noncommutative ring theory related to Morita equivalence is that of central separable or Azumaya algebras. For such an Azumaya algebra A, its Hochschild cohomology HH^*(A,A) is concentrated in degree 0 and is equal to the center of A. We introduce a notion of topological Azumaya algebra and show that in the case when the ground S-algebra R is an Eilenberg-Mac Lane spectrum of a commutative ring this notion specializes to classical Azumaya algebras. A canonical example of a topological Azumaya R-algebra is the endomorphism R-algebra F_R(M,M) of a finite cell R-module. We show that the spectrum of mod 2 topological K-theory KU/2 is a nontrivial topological Azumaya algebra over the 2-adic completion of the K-theory spectrum widehat{KU}_2. This leads to the determination of THH(KU/2,KU/2), the topological Hochschild cohomology of KU/2. As far as we know this is the first calculation of THH(A,A) for a noncommutative S-algebra A. | | Source: | arXiv, math.AT/0209003 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER