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SEMINAR: Groups and Combinatorics Seminar: Involutions in Automorphism Groups

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Today's date is Friday, March 29, 2024
Groups and Combinatorics Seminar: Involutions in Automorphism Groups Other events...
Phill Schultz

will speak on

Involutions in Automorphism Groups

at 1pm in Maths Lecture Room 1 on Tuesday 22nd of September.

Abstract: Let M be a module over a unital ring, and let M = A + B be a decomposition of M as a direct sum. Then Aut(M) contains the involution which is the identity on A and the map b maps to -b on B.

I identify a class of modules for which this mapping from decompositions to involutions is a bijection. For this class, I use properties of involutions to answer several problems in Module Theory; for example:

Which modules decompose as a direct sum of indecomposables? For which modules is such a decomposition unique up to isomorphism?

Kaplansky's Test Problems:

If N is isomorphic to a summand of M, and M to a summand of N, are N and M isomorphic? If M + M is isomorphic to N + N, is M isomorphic to N? If M + A is isomorphic to N + A, is M isomorphic to N?

All welcome
Speaker(s) Phill Schultz
Location Maths Lecture Room 1
Contact Michael Giudici <[email protected]>
Start Tue, 22 Sep 2009 13:00
End Tue, 22 Sep 2009 13:45
Submitted by Michael Giudici <[email protected]>
Last Updated Fri, 18 Sep 2009 09:30
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