Iwasawa decomposition of the Lie supergroup $SL(n,m,\mathbb{C})$

A note on Iwasawa-type decomposition

We study the Iwasawa-type decomposition of an open subset of SL(n,C) as SU(p,q)AN. We show that the dressing action of SU(p,q) is globally defined on the space of admissible elements in AN. We also show that the space of admissible elements is a multiplicative subset of AN. We establish a geometric criterion: the symmetrization of an admissible element maps the positive cone in C^n into itself.

关于某些Iwasawa代数的完整商环的Wedderburn分解

On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras

本文研究了某些Iwasawa代数的完整商环的Wedderburn分解，通过与群环的分解联系，在分枝假设下确定其结构。

关于某些Iwasawa代数的总商环的Wedderburn分解 II

On the Wedderburn decomposition of the total ring of quotients of certain Iwasawa algebras II

本文研究了某些Iwasawa代数的总商环的Wedderburn分解，通过群环的分解来全面确定其结构。

On derivations of subalgebras of real semisimple Lie algebras

Let $\mathfrak{g}$ be a real semisimple Lie algebra with Iwasawa decomposition $\mathfrak{k} \oplus \mathfrak{a} \oplus \mathfrak{n}$. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra $\mathfrak{n}$ that preserves its restricted root space decomposition is of the form $\text{ad}( W)$, where $W \in \mathfrak{m}\oplus .