Multiplicative properties of certain elements in Bridgeland's Hall algebras

TL;DR

This paper introduces specific elements in Bridgeland's Hall algebra for finite-dimensional algebras and proves a multiplication theorem, extending previous main results in the field.

Contribution

It presents a new class of elements in Bridgeland's Hall algebra and establishes their multiplication properties, generalizing prior key results.

Findings

Established a multiplication theorem for new elements in Bridgeland's Hall algebra

Generalized previous main results in the literature

Provides a framework for further algebraic exploration

Abstract

Let $A$ be a finite dimensional algebra of finite global dimension over a finite field. In the present paper, we introduce certain elements in Bridgeland's Hall algebra of $A$, and give a multiplication theorem of these elements. In particular, this generalizes the main result in $[4]$.