Antimonotonous quadratic forms and partially ordered sets

On the Auslander-Reiten quiver for the category of representations of partially ordered sets with an involution

In this article we describe the Auslander-Reiten quiver for some posets with an involution, that we call types $\mathfrak{U}_n$ and $\mathfrak{U}_\infty$. These posets appear in the differentiation III of Zavadskij [12]. We follow the approach to classical Auslander-Reiten theory due to Auslander, Reiten and Smalø[1]. For this purpose, we give a natural exact structure for the category of representations of a partially ordered set with an involution. We describe the projective and injective representations

Dimensions of finite type for representations of partially ordered sets

We consider the dimensions of finite type of representations of a partially ordered set, i.e. such that there is only finitely many isomorphism classes of representations of this dimension. We give a criterion for a dimension to be of finite type. We also characterize those dimensions of finite type, for which there is an indecomposable representation of this dimension, and show that there can be at most one indecomposable representation of any dimension of finite type. Moreover, if such a representation exists, it only has scalar endomorphisms.

On the unitarization of linear representations of primitive partially ordered sets

We describe all weights which are appropriated for the unitarization of linear representations of primitive partially ordered sets of finite type.

与有限偏序集相关的bocs的Burt-Butler代数

Burt-Butler algebras of the bocs associated to a finite partially ordered set

该研究针对有限偏序集对应的bocs，用关联代数及其平衡版本刻画了Burt-Butler代数，同时揭示其拟遗传结构、给出Ringel对偶的有界箭图表示、描述A的正合Borel子代数嵌入并刻画相关诱导与余诱导模子范畴。

Adjoint Functors, Projectivization, and Differentiation Algorithms for Representations of Partially Ordered Sets

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial construction of the derived set and for the differentiation functor

A Self-Dual Hopf Algebra on Double Partially Ordered Sets

Let $\mathbf D$ be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On $\BZ\mathbf D$ we define a product and a coproduct, together with an internal product, that is, degree-preserving. With these operations $\BZ\mathbf D$ is a Hopf algebra, self-dual with respect to a scalar product which counts the number of pictures (in the sense of Zelevinsky) between two double posets. The product and coproduct correspond respectively to disjoint union of posets and to a natural decomposition of a poset into order ideals. Restricting to sp…