by Yang, Dong

Let A be a finitary algebra over a finite field k, and A-$\text{mod}$ the category of finite dimensional left A-modules. Let $\mathcal{H}(A)$ be the corresponding Hall algebra, and for a positive integer r let D

_r
(A) be the subspace of $\mathcal{H}(A)$ which has a basis consisting of isomorphism classes of modules in A-$\text{mod}$ with at least r + 1 indecomposable direct summands. If A is the path algebra of the quiver of type A

_n
with linear orientation, then D

_r
(A) is known to be the kernel of the map from the twisted Hall algebra to the quantized Schur algebra indexed by n + 1 and r. For any A, we determine necessary and sufficient conditions for D

_r
(A) to be an ideal and some conditions for D

_r
(A) to be a subring of $\mathcal{H}(A)$. For A the path algebra of a quiver, we also determine necessary and sufficient conditions for D

_r
(A) to be a subring of $\mathcal{H}(A)$.

DOI: 10.1007/s10468-007-9069-y
Online Date: 9/26/2007
Print publication date: 12/1/2007
View article on SpringerLink

by Bonnafé, C.

We study some aspects of the representation theory of Mantaci–Reutenauer algebras: Cartan matrix, Loewy length, modular representations.

DOI: 10.1007/s10468-007-9074-1
Online Date: 9/22/2007
Print publication date: 8/1/2008
View article on SpringerLink

by Riley, David; Usefi, Hamid

Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ≅ U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.

DOI: 10.1007/s10468-007-9083-0
Online Date: 9/20/2007
Print publication date: 12/1/2007
View article on SpringerLink