DOI

Multiloop Lie algebras are twisted forms of classical (Chevalley) simple Lie algebras over a ring of Laurent polynomials in several variables k[x±1 1 , … , x±1 n].These algebras occur as centreless cores of extended affine Lie algebras (EALA’s) which are higher nullity generalizations of affine Kac-Moody Lie algebras. Such a multiloop Lie algebra L, also called a Lie torus, is naturally graded by a finite root system Δ, and thus possess a significant supply of nilpotent elements. We compute the difference between the full automorphism group of L and its subgroup generated by exponents of nilpotent elements. The answer is given in terms of Whitehead groups, also called non-stable K1-functors, of simple algebraic groups over the field of iterated Laurent power series k((x1)) … ((xn)). As a corollary, we simplify one step in the proof of conjugacy of Cartan subalgebras in EALA’s due to Chernousov, Neher, Pianzola and Yahorau, under the assumption rank(Δ) ≥ 2.

Язык оригиналаанглийский
Название основной публикацииLie Theory and Its Applications in Physics
РедакторыVladimir Dobrev
ИздательSpringer Nature
Страницы531-538
Число страниц8
Том191
ISBN (печатное издание)9789811026355
DOI
СостояниеОпубликовано - 1 янв 2016
СобытиеProceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015 - Varna, Болгария
Продолжительность: 15 июн 201521 июн 2015

конференция

конференцияProceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015
Страна/TерриторияБолгария
ГородVarna
Период15/06/1521/06/15

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