1. CMB Online first
 Bavula, V. V.; Lu, T.

Classification of simple weight modules over the SchrÃ¶dinger algebra
A classification of simple weight modules over the SchrÃ¶dinger
algebra is given. The Krull and the global dimensions are found
for the centralizer $C_{\mathcal{S}}(H)$ (and some of its prime factor
algebras) of the Cartan element $H$ in the universal enveloping
algebra $\mathcal{S}$ of the SchrÃ¶dinger (Lie) algebra. The simple
$C_{\mathcal{S}}(H)$modules are classified. The Krull and the global
dimensions are found for some (prime) factor algebras of the
algebra $\mathcal{S}$ (over the centre). It is proved that some (prime)
factor algebras of $\mathcal{S}$ and $C_{\mathcal{S}}(H)$ are tensor homological/Krull
minimal.
Keywords:weight module, simple module, centralizer, Krull dimension, global dimension, tensor homological minimal algebra, tensor Krull minimal algebra Categories:17B10, 17B20, 17B35, 16E10, 16P90, 16P40, 16P50 

2. CMB 2014 (vol 57 pp. 735)
 Cagliero, Leandro; Szechtman, Fernando

On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras
We describe of all finite
dimensional uniserial representations of a commutative associative
(resp. abelian Lie) algebra over a perfect (resp. sufficiently
large perfect) field. In the Lie case the size of the field
depends on the answer to following question, considered and solved
in this paper. Let $K/F$ be a finite separable field extension
and
let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some
nonzero elements $\alpha,\beta\in F$?
Keywords:uniserial module, Lie algebra, associative algebra, primitive element Categories:17B10, 13C05, 12F10, 12E20 

3. CMB 2007 (vol 50 pp. 603)
 Penkov, Ivan; Zuckerman, Gregg

Construction of Generalized HarishChandra Modules with Arbitrary Minimal $\mathfrak k$Type
Let $\mathfrak g$ be a semisimple complex Lie algebra and $\k\subset\g$ be
any algebraic subalgebra reductive in $\mathfrak g$. For any simple
finite dimensional $\mathfrak k$module $V$, we construct simple
$(\mathfrak g,\mathfrak k)$modules $M$ with finite dimensional $\mathfrak k$isotypic
components such that $V$ is a $\mathfrak k$submodule of $M$ and the Vogan
norm of any simple $\k$submodule $V'\subset M, V'\not\simeq V$, is
greater than the Vogan norm of $V$. The $(\mathfrak g,\mathfrak k)$modules
$M$ are subquotients of the fundamental series of
$(\mathfrak g,\mathfrak k)$modules.
Categories:17B10, 17B55 

4. CMB 2005 (vol 48 pp. 587)
 Lopes, Samuel A.

Separation of Variables for $U_{q}(\mathfrak{sl}_{n+1})^{+}$
Let $U_{q}(\SL)^{+}$ be the positive part of the quantized enveloping
algebra $U_{q}(\SL)$. Using results of AlevDumas and Caldero related
to the center of $U_{q}(\SL)^{+}$, we show that this algebra is free
over its center. This is reminiscent of Kostant's separation of
variables for the enveloping algebra $U(\g)$ of a complex semisimple
Lie algebra $\g$, and also of an analogous result of JosephLetzter
for the quantum algebra $\Check{U}_{q}(\g)$. Of greater importance to
its representation theory is the fact that $\U{+}$ is free over a
larger polynomial subalgebra $N$ in $n$ variables. Induction from $N$
to $\U{+}$ provides infinitedimensional modules with good properties,
including a grading that is inherited by submodules.
Categories:17B37, 16W35, 17B10, 16D60 
