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Title: Involutive automorphisms and real forms of Kac-Moody algebras
Author: Clarke, Stefan
Awarding Body: University of St Andrews
Current Institution: University of St Andrews
Date of Award: 1996
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Involutive automorphisms of complex affine Kac-Moody algebras (in particular, their conjugacy classes within the group of all automorphisms) and their compact real forms are studied, using the matrix formulation which was developed by Cornwell. The initial study of the a(1) series of affine untwisted Kac-Moody algebras is extended to include the complex affine untwisted Kac-Moody algebras B(1), C(1) and D(1). From the information obtained, explicit bases for real forms of these Kac-Moody algebras are then constructed. A scheme for naming some real forms is suggested. Further work is included which examines the involutive automorphisms and the real forms of A2(2)and the algebra G(1)2 (which is based upon an exceptional simple Lie algebra). The work involving the algebra A2(2)is part of work towards extending the matrix formulation to twisted Kac-Moody algebras. The analysis also acts as a practical test of this method, and from it we may infer different ways of using the formulation to eventually obtain a complete picture of the conjugacy classes of the involutive automorphisms of all the affine Kac-Moody algebras.
Supervisor: Cornwell, J. F. Sponsor: Science and Engineering Research Council (SERC) ; Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA252.3K2C6 ; Kac-Moody algebras