Simplicity of some twin tree automorphism groups with trivial commutation relations

We prove simplicity for incomplete rank 2 Kac-Moody groups over algebraic closures of finite fields with trivial commutation relations between root groups corresponding to prenilpotent pairs. We don't use the (yet unknown) simplicity of the corresponding finitely generated groups (i.e., when the ground field is finite). Nevertheless we use the fact that the latter groups are just infinite (modulo center).Comment: 10 page

Fiscal Policy under the Debt Feedback Rule: The Case of Japan

The Japanese government has amassed a huge amount of gross public debts over the past several decades. However, previous empirical works dealing with vector auto-regression (VAR) have not considered the effect of debt on fiscal policy and the macro economy. In this paper, we incorporate debt dynamics in a VAR model in the spirit of Favero and Giavazzi (2007, 2011). The inclusion of the debt feedback rule in VAR can help overcome the misspecification problem and provide direction toward a more relevant debt path and fiscal stance. The main findings of our study are as follows. First, in the pre-bubble period, the fiscal authority in Japan increased the primary surplus when the public debt level was high. However, this Ricardian behavior was not seen in the post-bubble period. Second, the impulse response functions to the expansionary government spending shock reveal that the stance of fiscal policy was more active in the pre-bubble. Third, while the forecast of debt dynamics in the pre-bubble period was stable, it became explosive in the post-bubble period.fiscal policy, Japan's public debt, VAR

Word maps in Kac-Moody setting

The paper is a short survey of recent developments in the area of word maps evaluated on groups and algebras. It is aimed to pose questions relevant to Kac--Moody theory.Comment: 16 pag

Elementary equivalence of Kac-Moody groups

The paper is devoted to model-theoretic properties of Kac-Moody groups with the focus on elementary equivalence of Kac-Moody groups. We show that elementary equivalence of (untwisted) affine Kac-Moody groups implies coincidence of their generalized Cartan matrices and the elementary equivalence of their ground fields. We also show that elementary equivalence of arbitrary Kac-Moody groups over finite fields implies coincidence of these fields and an isomorphism of their twin root data. The similar result is established for Kac-Moody groups defined over infinite subfields of the algebraic closures of finite fields.Comment: 10 page

Affine Kac-Moody Groups as Twisted Loop Groups obtained by Galois Descent Considerations

We provide explicit generators and relations for the affine Kac-Moody groups, as well as a realization of them as (twisted) loop groups by means of Galois descent considerations. As a consequence, we show that the affine Kac-Moody group of type X(r) N is isomorphic to the fixed-point subgroup of the affine Kac-Moody group of type X(1) N under an action of the Galois group

Chevalley groups over Dedekind domains and some problems for K₂(2,ℤₛ)

We review Chevalley groups over Dedekind domains and associated K₂ groups. We also recall some old results on K₂(2,ℤₛ). Then, we show here several new examples and computations