Tokyo Journal of Mathematics

Groups Defined by Extended Affine Lie Algebras with Nullity $2$

Jun MORITA and Hideyuki SAKAGUCHI

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Abstract

After certain completions, we define adjoint groups of extended affine Lie algebras with nullity $2$. Then we show that such groups have Tits systems with affine Weyl groups (Part I). This idea allows us to consider linear groups over some completed quantum tori. By the same argument, we can prove that these linear groups also have Tits systems with affine Weyl groups. Using this fact we will study their universal central extensions as well as associated $K_1$-groups and $K_2$-groups (Part II). We will discuss some relationship among our groups constructed here (Part III).

Article information

Source
Tokyo J. Math., Volume 29, Number 2 (2006), 347-383.

Dates
First available in Project Euclid: 1 February 2007

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1170348172

Digital Object Identifier
doi:10.3836/tjm/1170348172

Mathematical Reviews number (MathSciNet)
MR2284977

Zentralblatt MATH identifier
1213.17025

Subjects
Primary: 17B65: Infinite-dimensional Lie (super)algebras [See also 22E65]
Secondary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24]

Citation

MORITA, Jun; SAKAGUCHI, Hideyuki. Groups Defined by Extended Affine Lie Algebras with Nullity $2$. Tokyo J. Math. 29 (2006), no. 2, 347--383. doi:10.3836/tjm/1170348172. https://projecteuclid.org/euclid.tjm/1170348172


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