σ-monogenic functions in commutative algebras

Abstract

In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.

Keywords

• commutative associative algebra
• monogenic function
• $\sigma$-monogenic function
• constructive description of $\sigma$-monogenic function
• generalization of pseudoanalytic functions
• generalization of $(p,q)$-analytic functions