Trace Formulas, Invariant Bilinear Forms and Dynkin Indices of Lie Algebra Representations Over Rings

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Title: Trace Formulas, Invariant Bilinear Forms and Dynkin Indices of Lie Algebra Representations Over Rings
Authors: Pham, Khoa
Date: 2014
Abstract: The trace form gives a connection between the representation ring and the space of invariant bilinear forms of a Lie algebra $L$. This thesis reviews the definition of the trace of an endomorphism of a finitely generated projective module over a commutative ring $R$. We then use this to look at the trace form of a finitely generated projective representation of a Lie algebra $L$ over $R$ and its representation ring. While doing so, we prove a few trace formulas which are useful in the theory of the Dynkin index, an invariant introduced by Dynkin in 1952 to study homomorphisms between simple Lie algebras.
URL: http://hdl.handle.net/10393/31502
http://dx.doi.org/10.20381/ruor-6577
CollectionThèses, 2011 - // Theses, 2011 -
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