
We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.
35 pages
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Algebra and Number Theory, Rings and Algebras (math.RA), FOS: Mathematics, Graded Lie (super)algebras, 17B40 (Primary) 17A36, 17B67 (Secondary), Mathematics - Rings and Algebras, Representation Theory (math.RT), Mathematics - Representation Theory
Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Algebra and Number Theory, Rings and Algebras (math.RA), FOS: Mathematics, Graded Lie (super)algebras, 17B40 (Primary) 17A36, 17B67 (Secondary), Mathematics - Rings and Algebras, Representation Theory (math.RT), Mathematics - Representation Theory
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