Modules of polynomial Rota-Baxter Algebras and matrix equations

2020/03/12 by Tang, Xiaomin · 1 citation
#12H20 #16W99 #45N05 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.05630

Abstract

The all Rota-Baxter algebra structures on the polynomial algebra R=\bf k[x] are well known. We study the finite dimensional modules of polynomial Rota-Baxter algebras (\bfk[x],P) or (x \bf k [x],P) of weight nonzero since some cases of weight zero have been studied. The main result shows that every module over the polynomial Rota-Baxter algebra (\bfk[x],P) or (x \bf k [x],P) is equivalent to the modules over a plane \bf k⟨ x,y ⟩/ I where I is some ideal of free algebra \bf k⟨ x,y ⟩. Furthermore, we provide the classification of modules of polynomial Rota-Baxter algebras of weight nonzero through solution to some matrix equation.

Cited by

• Linear-in-degree monomial Rota-Baxter of weight zero and averaging operators on F[x, y] and F₀[x, y]

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