In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront with questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.

The algebra of slice functions / Ghiloni, R.; Perotti, A.; Stoppato, C.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 369:7(2017), pp. 4725-4762. [10.1090/tran/6816]

The algebra of slice functions

Ghiloni R.;Perotti A.;
2017-01-01

Abstract

In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative *-algebra A over R. These recently introduced function theories generalize to higher dimensions the classical theory of functions of a complex variable. Slice functions over A, which comprise all polynomials over A, form an alternative *-algebra themselves when endowed with appropriate operations. We presently study this algebraic structure in detail and we confront with questions about the existence of multiplicative inverses. This study leads us to a detailed investigation of the zero sets of slice functions and of slice regular functions, which are of course of independent interest.
2017
7
Ghiloni, R.; Perotti, A.; Stoppato, C.
The algebra of slice functions / Ghiloni, R.; Perotti, A.; Stoppato, C.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 369:7(2017), pp. 4725-4762. [10.1090/tran/6816]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/97868
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