Diagonal reduction algebras of $\gl$ type

TL;DR

This paper investigates the structure and properties of diagonal reduction algebras associated with the Lie algebra gl_n, highlighting stabilization phenomena and providing complete defining relations.

Contribution

It introduces a stabilization phenomenon for these algebras and explicitly lists their complete sets of defining relations, advancing understanding of their algebraic structure.

Findings

Established a stabilization phenomenon for diagonal reduction algebras.

Provided complete sets of defining relations for these algebras.

Discussed properties related to rings of definition and algorithmic relations.

Abstract

Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra $gl_n$ into $gl_n \oplus gl_n$, we establish a stabilization phenomenon and list the complete sets of defining relations.