Modules of free commutative non-unital Rota-Baxter algebras

发布时间：2022-03-24 来源：赢咖3 浏览次数：

Speaker:	唐孝敏	DateTime:	2022年3月29日(周二)上午10：00-11:00
Brief Introduction to Speaker: 唐孝敏，黑龙江大学。		Place:	腾讯会议：622183370
Abstract:In this talk, we study the free commutative non-unital Rota-Baxter algebra (R, P) which is the algebra of polynomials in one variable without constant term with Rota-Baxter operators of nonzero weight. The main result shows that every module over the Rota-Baxter algebra (R, P) is equivalent to the modules over a plane k_0/I where I is some ideal of the non-unital free algebra k_0. Furthermore, we provide the classification of modules (R, P) of weight nonzero through solution to the matrix equation ɑAB=BAB+(ɑ+1)BA. We also prove that there exists only 1-dimensional irreducible module, and the indecomposable module can be of any dimension.