Topological Hochschild homology of twisted group algebras

Let G be a group and A be a ring. There is a stable equivalence of orthogonal spectra ... between the topological Hochschild homology of the group algebra A[G] and the smash product of the topological Hochschild homology of A and the cyclic bar construction of G. This thesis generalizes this result to a twisted group algebra AT[G]. As an A-module, Ar[G] = A[G], but the multiplication is given by ag. a'g' = ag(a') gg', where G acts on A from the left through ring automorphisms. The main result is given in terms of a variant THH9(A) of the topological Hochschild spectrum that is equipped with a twisted cyclic structure inherited from the cyclic structure of the cyclic pointed space THH(A)[-]. We first define a parametrized orthogonal spectrum E(A, G) over the cyclic bar construction NCY(G). We prove there is a stable equivalence of spectra between the associated Thom spectrum of E(A, G) and THH(AT[G]). We then prove there is a stable equivalence of orthogonal spectra ... where the wedge-sum on the left hand side ranges over the conjugacy classes of elements of G and the equivalence depends on a choice of representative g E (g) of every conjugacy class of elements in G.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Vera, Daniel Joseph

Advisor dc:contributor.advisor

• Lars Hesselholt.

• Mathematics.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/34615

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/34615