2026-09-21T09:25:28Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/346152022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Lars Hesselholt.
Vera, Daniel Joseph
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-11-07T13:36:22Z
2006-11-07T13:36:22Z
2006
2006
http://hdl.handle.net/1721.1/34615
71329129
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 61-62).
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.
by Daniel Joseph Vera.
Ph.D.
62 p.
2110537 bytes
2113037 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Topological Hochschild homology of twisted group algebras
Thesis
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