Rota–Baxter operators on 4-dimensional complex simple associative algebras

Rota-type operators on 3-dimensional nilpotent associative algebras

“…Rota-Baxter operators were defined by Baxter to solve an analytic formula in probability [2], [7], [9], [10]. It has been related to other areas in mathematics and mathematical physics [1], [3], [5], [15], [21] A Rota-Baxter operator on an associative algebra A over a field F is defined to be a linear map P : A → A satisfying P (x)P (y) = P (xP (y) + P (x)y + λxy), ∀x, y ∈ A, λ ∈ F.…”

Classification of Rota-Baxter operators on semigroup algebras of order two and three

“…Even there computations are quite complicated. In recent years, some progress regarding such computations has been achieved, with applications to pre-Lie algebras, dendriform algebras and the classical Yang-Baxter equation [1,28,35,43]. In this paper, we study Rota-Baxter operators on a class of low dimensional algebras, namely semigroup algebras for small order semigroups.…”

“…Because of the complex nature of Rota-Baxter operators, determining their classification by hand is challenging even for low dimensional algebras, as observed in [1,28,43]. In such a case, computer algebra provides an indispensable aid for both predicting and verifying these operators.…”

Post-Lie Algebra Structures on the Witt Algebra

“…As a matter of fact, the Rota-Baxter operators were originally defined on associative algebras by G. Baxter to solve an analytic formula in probability [2] and then developed by the Rota school [16]. These operators have showed up in many areas in mathematics and mathematical physics (see [6,11,12,18] and the references therein). * Corresponding author: X. Tang.…”