SEMINAR: Groups and Combinatorics Seminar: Involutions in Automorphism Groups
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Groups and Combinatorics Seminar: Involutions in Automorphism Groups |
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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
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Location |
Maths Lecture Room 1
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Contact |
Michael Giudici
<[email protected]>
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Start |
Tue, 22 Sep 2009 13:00
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End |
Tue, 22 Sep 2009 13:45
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Submitted by |
Michael Giudici <[email protected]>
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Last Updated |
Fri, 18 Sep 2009 09:30
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