Self-adjoint (a,b)-modules and hermitian forms
Singularity Theory
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In this thesis we analyse the behaviour of (a,b)-modules under the action of the duality functors. We are mostly interested in the existence of self-adjoint (a,b)-modules admitting an hermitian form, which we show is not a trivial condition: every self-adjoint regular (a,b)-module can be split into the direct sum of hermitian (a,b)-modules and (a,b)-modules admitting only an anti-hermitian form. This result leads us to the proof of existence of self-dual Jordan-Hölder composition series for regular self-adjoint (a,b)-modules and we provide, following Ridha Belgrade, an alternative proof of th...
In this thesis we analyse the behaviour of (a,b)-modules under the action of the duality functors. We are mostly interested in the existence of self-adjoint (a,b)-modules admitting an hermitian form, which we show is not a trivial condition: every self-adjoint regular (a,b)-module can be split into the direct sum of hermitian (a,b)-modules and (a,b)-modules admitting only an anti-hermitian form. This result leads us to the proof of existence of self-dual Jordan-Hölder composition series for regular self-adjoint (a,b)-modules and we provide, following Ridha Belgrade, an alternative proof of the existence of Kyoji Saito's higher residue pairings .
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