Modular adjacency algebras of Dual polar schemes

TL;DR

This paper investigates the structure of adjacency algebras of dual polar schemes over fields of positive characteristic, focusing on cases where these algebras are local, expanding understanding of their algebraic properties.

Contribution

It provides a detailed analysis of the adjacency algebras of dual polar schemes over positive characteristic fields, especially characterizing when they are local algebras.

Findings

Determined the structure of adjacency algebras when they are local.

Extended the understanding of adjacency algebras over positive characteristic fields.

Identified conditions under which these algebras are semisimple or not.

Abstract

We can define the adjacency algebra of an association scheme over arbitrary field. It is not always semisimple over a field of positive characteristic. The structures of adjacency algebras over a field of positive characteristic have not been sufficiently studied. In this paper, we consider the structures of adjacency algebras of dual polar schemes over a field of positive characteristic and determine them when their algebras are local algebras.