Characteristics of Rota–Baxter algebras

Abstract

The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota–Baxter algebra, called the Rota–Baxter characteristic. We introduce an invariant, called the ascent set, of a Rota–Baxter characteristic, which allows us to classify Rota–Baxter characteristics in the homogenous case and relate Rota–Baxter characteristics in general to the homogeneous case through initial ideals. A more detailed study is given to Rota–Baxter characteristics with special base rings, including prime Rota–Baxter characteristics and the principle generation of Rota–Baxter characteristics.

Keywords:

• Rota–Baxter algebra
• Rota–Baxter characteristic
• initial object
• initial ideal
• prime ideal

2010 Mathematics Subject Classification:

• 13C05
• 13E05
• 16W99

Additional information

Funding

This work was supported by National Natural Science Foundation (Grant Nos. 11501467 and 11771190). H. Yu would like to express his appreciation to Prof. Gaoyong Zhang and New York University for hospitality and support.