Constructing cell data for diagram algebras

Cellularity of diagram algebras as twisted semigroup algebras

The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups. This theorem, which generalises a recent result of East about semigroup algebras of inverse semigroups, allows us to easily reproduce the cellularity of these algebras.

Cellularity of Cyclotomic Birman--Wenzl--Murakami algebras

We show that the cyclotomic Birman-Wenzl-Murakami algebras are cellular by producing a cellular basis of affine tangle diagrams.

分区代数的细胞子代数

Cellular subalgebras of the partition algebra

本文研究分区代数等图代数的细胞结构，利用半图分解证明相关图代数均为细胞代数并参数化其细胞模，同时提出从一般细胞代数与 rook Brauer 代数子代数构造新细胞代数的 cellular wreath product 方法。

Sandwich cellularity 和 cell theory 的一种版本

Sandwich cellularity and a version of cell theory

本文探讨了sandwich cellular algebra理论作为代数cell theory的版本，并应用于Hecke代数等多种代数结构。

Constructing simply laced Lie algebras from extremal elements

For any finite graph Gamma and any field K of characteristic unequal to 2 we construct an algebraic variety X over K whose K-points parameterise K-Lie algebras generated by extremal elements, corresponding to the vertices of the graph, with prescribed commutation relations, corresponding to the non-edges. After that, we study the case where Gamma is a connected, simply laced Dynkin diagram of finite or affine type. We prove that X is then an affine space, and that all points in an open dense subset of X parameterise Lie algebras isomorphic to a single fixed Lie algebra. If Gamma is of affine t…

图示Okada幺半群与Okada代数的胞腔性

Diagrammatic Okada monoid and cellularity of the Okada algebra

本文利用带标记非交叉弧图实现Okada代数与Okada幺半群，证明其维数、正则性等性质，构造其胞腔基并提出相关猜想，推进对称群与Okada代数的类比研究。