Self-adjoint (a,b)-modules and hermitian forms - Singularity Theory

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 .

About the author

Piotr P. Karwasz is alumnus of the École Normale Supérieure of Paris and received his Ph.D. at the university of Nancy. He is an Assistant Professor at the University of Gdäsk, Poland.

Product details

• Authors: Piotr Karwasz
• Publisher: LAP Lambert Academic Publishing
• Languages: English, German
• Product format: Paperback / Softback
• Released: 19.10.2012
• EAN: 9783659238383
• ISBN: 978-3-659-23838-3
• No. of pages: 76
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra