A note on a Hecke ring associated with the Heisenberg Lie algebra

TL;DR

This paper explores the generalization of Hecke rings from classical groups to automorphism groups of algebras, and specifically develops an analog for the Heisenberg Lie algebra, expanding the theoretical framework.

Contribution

It introduces a new perspective by extending Hecke ring theory to automorphism groups of algebras, with a focus on the Heisenberg Lie algebra case.

Findings

Established an analog of classical Hecke theory for the Heisenberg Lie algebra

Generalized Hecke rings to automorphism groups of certain algebras

Provided foundational results for future algebraic and number-theoretic research

Abstract

This paper focuses on the theory of the Hecke rings associated with the general linear groups originally studied by Hecke and Shimura et al., and moreover generalizes its notions to Hecke rings associated with the automorphism groups of certain algebras. Then, in the case of the Heisenberg Lie algebra, we show an analog of the classical theory.