Rota-Baxter Type Operators on Algebras

"Linear operators play essential role in modern mathematical and physical sciences. The notion of Rota-Baxter operator as
natural generalization of by parts integration formula arises in a seminal paper of G. Baxter.
The linear map P: A → A on an algebra A is called a Rota-Baxter operator of weight λ if
P(x) · P(y) = P (xP(y) + P(x)y + λxy).
This project studies Rota-Baxter type operators on algebras. The description of Rota-Baxter operators and other Rota-type
operators is a major problem.
Let A = F G be the group algebra of a finite group G over a field F. Our aim is to investigate the properties of Rota-type
operators on the modular group algebra F G, i.e., algebras in which the characteristic of the ground field F divides the order
of the group G. Of particular interest is the case when the characteristic of F is two."