Note on The Generalized Derivation Tower Theorem for Lie algebras

Representation theory of towers of recollement: theory, notes, and examples

We give an axiomatic framework for studying the representation theory of towers of algebras. We introduce a new class of algebras, contour algebras, generalising (and interpolating between) blob algebras and cyclotomic Temperley-Lieb algebras. We demonstrate the utility of our formalism by applying it to this class.

A Note on Derivations of Lie Algebras

In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is necessarily solvable. As a result, if $L$ has a derivation $d:L\to L$, such that $L^n\subseteq d(L)$, for some $n\geq 1$, then $L$ is solvable.

广义三角矩阵环上的Jordan导子

Jordan Derivation On Generalized Triangular Matrix Rings

本文证明了广义三角矩阵环上的任意Jordan导子均为导子，推广了Brešar等人的已知结果。