Isomorphisms of Chevalley Groups over Algebras

Automorphisms and Isomorphisms of Chevalley Groups and Algebras

Suppose that Φ is a reduced irreducible root system, R is an associative commutative ring with unity, G(Φ, R) is the corresponding adjoint Chevalley group, and E(Φ, R) is its elementary subgroup (see Section 5). There are a lot of results (see, e.g., [Wat80], [Pet82], [GMi83], [HO’M89], [Abe93], [Che00], [Bun07], and references therein*) asserting that, under some conditions, all automorphisms ...

Chevalley Groups over Commutative Rings

Infinite Dimensional Chevalley Groups and Kac-moody Groups over Z

Let A be a symmetrizable generalized Cartan matrix. Let g be the corresponding Kac-Moody algebra. Let G(R) be Tits’ Kac-Moody group functor over commutative rings R associated to g. Then G(R) is given by five axioms KMG1-KMG5 which are natural extensions of the properties of Chevalley-Demazure group schemes. We give a construction of the Tits functor for symmetrizable Kac-Moody groups G using i...

Isomorphisms in unital $C^*$-algebras

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

Parametrized Braid Groups of Chevalley Groups

We introduce the notion of a braid group parametrized by a ring, which is defined by generators and relations and based on the geometric idea of painted braids. We show that the parametrized braid group is isomorphic to the semi-direct product of the Steinberg group (of the ring) with the classical braid group. The technical heart of the proof is the Pure Braid Lemma 2.1.1, which asserts that c...