Self-injective cellular algebras of polynomial growth representation type

Ziegler Spectra of Self Injective Algebras of Polynomial Growth

A description of the Ziegler spectrum is given for trivial extensions of tubular algebras and related self-injective algebras of tubular type.

A Reciprocity Result for Projective Indecomposable Modules of Cellular Algebras and BGG Algebras

We show that an adaptation of Landrock's Lemma for symmetric algebras also holds for cellular algebras and BGG algebras. This is a result relating the radical layers of any two projective modules. The reason it holds in our setting is that there is a duality between injective hulls and projective covers. As a corollary we deduce that BGG reciprocity respects Loewy structure.

Hochschild cohomology for periodic algebras of polynomial growth

We describe the dimensions of low Hochschild cohomology spaces of exceptional periodic representation-infinite algebras of polynomial growth. As an application we obtain that an indecomposable non-standard periodic representation-infinite algebra of polynomial growth is not derived equivalent to a standard self-injective algebra.

Cores of graded algebras with triangular decomposition

We consider self-injective finite-dimensional graded algebras admitting a triangular decomposition. In a preceding paper, we have shown that the graded module category of such an algebra is a highest weight category and has tilting objects in the sense of Ringel. In this paper we focus on the degree zero part of the algebra, the core of the algebra. We show that the core captures essentially all relevant information about the graded representation theory. Using tilting theory, we show that the core is cellular. We then describe a canonical construction of a highest weight cover, in the sense o…

Derived equivalences, restriction to self-injective subalgebras and invariance of homological dimensions

Derived equivalences between finite dimensional algebras do, in general, not pass to centraliser (or other) subalgebras, nor do they preserve homological invariants of the algebras, such as global or dominant dimension. We show that, however, they do so for large classes of algebras described in this article. Algebras $A$ of $ν$-dominant dimension at least one have unique largest non-trivial self-injective centraliser subalgebras $H_A$. A derived restriction theorem is proved: A derived equivalence between $A$ and $B$ implies a derived equivalence between $H_A$ and $H_B$. Two methods are devel…

$\mathbb G$-模的滤过与增长

Filtrations and Growth of $\mathbb G$-modules

研究正特征域上仿射群概形的无限维模，通过上升收敛序列给出函子性滤过，刻画内射模，并利用有限维子余代数限制定义新不变量，探讨余有限模的增长。