The suspension spectrum of a group can be thought of as a kind of group ring S[G]. It would be interesting to try to see how many of the classical results about Hopf-algebras (or just group rings) one could obtain for such objects.
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In other words, study "representation theory" for groups over the sphere spectrum S instead of any field.
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But that brings to mind a somewhat simpler problem I suppose: do people do representation theory over the integers? Is it too hard?
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Replying to @koszuldude
I was thinking about how positive integers are represented as combinations of other positive integers. There are additive and multiplicative partition functions. There's the integer complexity: https://en.wikipedia.org/wiki/Integer_complexity …
10:04 PM - 22 Feb 2019
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