Division algebras of slice functions

Abstract

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem.

24 pages, published online in Proc. Roy. Soc. Edinburgh Sect. A

References in corpus (1)

• Singularities of slice regular functions over real alternative *-algebras

Cited by in corpus (10)

• Slice regular functions in several variables
• Slice regularity and harmonicity on Clifford algebras
• Geometric function theory over quaternionic slice domains
• On a class of orientation-preserving maps of ${\mathbb{R}}^4$
• Almansi-type theorems for slice-regular functions on Clifford algebras
• Equivalence of slice semi-regular functions via Sylvester operators
• Slice conformality and Riemann manifolds on quaternions and octonions
• Eigenvalue problems for slice functions
• A four dimensional Bernstein Theorem
• Spherical coefficients of slice regular functions