Title
Quaternionic Hermitian spinor systems and compatibility conditionsQuaternionic Hermitian spinor systems and compatibility conditions
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Research group
Fundamental Mathematics
Publication type
article
Publication
Berlin,
Subject
Mathematics
Source (journal)
Advances in geometry. - Berlin
Volume/pages
11(2011):1, p. 169-189
ISSN
1615-715X
ISI
000286806600009
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
In this paper we show that the systems introduced in [[Eelbode, Adv. Appl. Clifford Algebr. 17: 635--649, 2007]] and [[Peñña-Peñña, Sabadini, Sommen, Complex Anal. Oper. Theory 1: 97--113, 2007]] are equivalent, both giving the notion of quaternionic Hermitian monogenic functions. This makes it possible to prove that the free resolution associated to the system is linear in any dimension, and that the first cohomology module is nontrivial, thus generalizing the results in [[Peñña-Peñña, Sabadini, Sommen, Complex Anal. Oper. Theory 1: 97--113, 2007]]. Furthermore, exploiting the decomposition of the spinor space into ( m)-irreducibles, we find a certain number of ''algebraic'' compatibility conditions for the system, suggesting that the usual spinor reduction is not applicable.
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