Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 017, 21 pages      arXiv:1502.07441      https://doi.org/10.3842/SIGMA.2015.017
Contribution to the Special Issue on New Directions in Lie Theory

On the Killing form of Lie Algebras in Symmetric Ribbon Categories

Igor Buchberger and Jürgen Fuchs
Teoretisk fysik, Karlstads Universitet, Universitetsgatan 21, S-65188 Karlstad, Sweden

Received September 30, 2014, in final form February 20, 2015; Published online February 26, 2015

Abstract
As a step towards the structure theory of Lie algebras in symmetric monoidal categories we establish results involving the Killing form. The proper categorical setting for discussing these issues are symmetric ribbon categories.

Key words: Lie algebra; monoidal category; ribbon category; Killing form; Lie superalgebra.

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