In Levstein and Maldonado (2007), the Terwilliger algebra of the Johnson scheme J(n,d) was determined when n≥3d. In this paper, we determine the Terwilliger algebra T for the remaining case 2d≤n<3d.

In this article we characterize the closed cones respectively generated by the symmetric inverse M-matrices and by the inverses of symmetric row diagonally dominant M-matrices. We show the latter has a finite number of ...

In 1996, Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite ...

A special question for noncommutative algebras is Zariski cancellation problem. In this thesis we establish cancellation for some special classes of algebras such as skew PBW extensions, some Artin--Schelter regular algebras ...

This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical ...

This thesis deals with a range of questions in combinatorial aspects of the representation theory of algebras and its applications. In particular, we provide a solution to the following problems: 1. How is it possible ...

The Jordan plane can be seen as a quotient algebra, as a graded Ore extension and as a graded skew PBW extension. Using these interpretations, it is proved that the Jordan plane is an Artin-Schelter regular algebra and a ...