Simplicity in bounded skew-power series rings.

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• Adam Jones, University of Cambridge
• Wednesday 04 December 2024, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

The notion of a skew-power series ring is not, in general, well-defined for an abstract ring, and it is not necessarily unique, it requires the coefficient ring R and the skew derivation (\sigma,\delta) to satisfy appropriate topological considerations. In this talk, I will explore a specific notion of a bounded skew-power series ring R^+[[x;\sigma,\delta]], illustrating why this notion is universal, and describing recent results which highlight algebraic properties of this structure, namely when it is a prime or even simple ring. These results are useful when studying the representation theory of a solvable, compact p-adic Lie group G, since the associated Iwasawa algebra \Omega(G) arises as a skew power series ring, and our results go some way towards classifying the prime ideals in this algebra. This is joint work with William Woods.

This talk is part of the Algebra and Representation Theory Seminar series.

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