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Register a new userReal forms and finite order automorphisms of affine Kac-Moody algebras - an outline of a new approach
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Ernst Heintze
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We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.
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This is a summary (in French) of my work about brownian motion and Kac-Moody algebras during the last seven years, presented towards the Habilitation degree.
This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included with figures illustrating the rank 2 cases. New results relating fusion coefficients to tensor product coefficients are proved, and a conjecture is given which shows that the Frenkel-Zhu affine fusion rule theorem can be seen as a beautiful generalization of the Parasarathy-Ranga Rao-Varadarajan tensor product theorem. Previous work of the author and collaborators on a different approach to fusion rules from elementary group theory is also explained.
We describe Hom-Lie structures on affine Kac-Moody and related Lie algebras, and discuss the question when they form a Jordan algebra.
We consider the subalgebras of split real, non-twisted affine Kac-Moody Lie algebras that are fixed by the Chevalley involution. These infinite-dimensional Lie algebras are not of Kac-Moody type and admit finite-dimensional unfaithful representations. We exhibit a formulation of these algebras in terms of $mathbb{N}$-graded Lie algebras that allows the construction of a large class of representations using the techniques of induced representations. We study how these representations relate to previously established spinor representations as they arise in the theory of supergravity.
In this note, we provide a complete description of the closed sets of real roots in a Kac-Moody root system.
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