Involutions of multicomplex numbers

Abstract: Given a real algebra $A$, a function $f : A \to A$ is called a (real)-linear involution if $f$ is (real)-linear and $f(f(a)) = a$ for any element $a \in A$. A natural question, at least when $\dim A < \infty$, is: How many (real)-linear involutions are there for a given complex algebra?

We will answer this question in the first part of the talk for the commutative real algebra $\mathbb{M}\mathbb{C}(n) (n \geq 1)$ of multicomplex numbers, a commutative generalization of the complex numbers. In the second part of the talk, I will show how to define different Laplacians using the (real)-linear involutions of the multicomplex numbers.

The first part of this talk is a joint work with Nicolas Doyon and William Verreault.

analysis of PDEsclassical analysis and ODEsfunctional analysisprobabilityspectral theory

Audience: researchers in the discipline

Quebec Analysis and Related Fields Graduate Seminar