Centralisers in Classical Lie Algebras
Lewis William Topley
TL;DR
This thesis explores properties of centralisers in classical Lie algebras, focusing on modular representation theory, sheets of simple Lie algebras, and the representation theory of finite W-algebras and enveloping algebras.
Contribution
It provides new insights into the structure and representation theory of centralisers in classical Lie algebras, connecting modular theory, sheets, and W-algebras.
Findings
Analysis of modular representation theory of centralisers
Characterization of sheets in simple Lie algebras
Results on the representation theory of finite W-algebras
Abstract
In this thesis we discuss some properties of centralisers in classical Lie algebas and related structures. Our results follow three distinct but related themes: the modular representation theory of centralisers, the sheets of simple Lie algebras and the representation theory of finite W-algebras and enveloping algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models