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Results tagged with rt.representation-theory
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user 40180
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
4
votes
1
answer
205
views
Bott periodicity homeomorphisms for spaces of Clifford extensions
I am trying to prove the following statement of real Bott periodicity, on the level of actual spaces of Clifford module extensions (i.e., not equivalence classes of modules).
Let $W = \mathbb{R}^{\in …
- 151
1
vote
Bott periodicity homeomorphisms for spaces of Clifford extensions
I believe I have the idea of a proof. Apologies for the mess - hopefully it is somewhat intelligible (and somewhat correct).
We follow the form of this isomorphism: $Cl_{n+8} \cong Cl_n\otimes_\math …
- 151
8
votes
1
answer
231
views
What is the inverse in K-theory represented by Clifford module extensions?
I am working on a model for topological KO-theory which is represented by explicit spaces of orthogonal Clifford module extensions. That is, assuming $M$ compact, $KO^{-n+1}(M) := [M,X_n]$ where the …
- 151
2
votes
Accepted
What is the inverse in K-theory represented by Clifford module extensions?
For what it's worth, I did eventually get the answer. The idea is to notice that if $\overline{W}$ denotes the background Clifford module $W$ (above $\mathbb{R}^n$) endowed with the opposite module s …
- 151