TY - GEN

T1 - Automorphisms of multiloop lie algebras

AU - Stavrova, Anastasia

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85009723885&partnerID=8YFLogxK

U2 - 10.1007/978-981-10-2636-2_40

DO - 10.1007/978-981-10-2636-2_40

M3 - Conference contribution

AN - SCOPUS:85009723885

SN - 9789811026355

VL - 191

SP - 531

EP - 538

BT - Lie Theory and Its Applications in Physics

A2 - Dobrev, Vladimir

PB - Springer Nature

T2 - Proceedings of the 11th International Workshop on Lie Theory and Its Applications in Physics, 2015

Y2 - 15 June 2015 through 21 June 2015

ER -