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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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IMPACT FACTOR 2017: 0.734

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1615-7168
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Volume 11, Issue 1

Issues

Quaternionic Hermitian spinor systems and compatibility conditions

Alberto Damiano / David Eelbode / Irene Sabadini
Published Online: 2011-01-07 | DOI: https://doi.org/10.1515/advgeom.2010.045

Abstract

In this paper we show that the systems introduced in [Eelbode, Adv. Appl. Clifford Algebr. 17: 635–649, 2007] and [Peña-Peña, 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 [Peña-Peña, Sabadini, Sommen, Complex Anal. Oper. Theory 1: 97–113, 2007]. Furthermore, exploiting the decomposition of the spinor space into 𝔰𝔭(m)-irreducibles, we find a certain number of “algebraic” compatibility conditions for the system, suggesting that the usual spinor reduction is not applicable.

About the article

Received: 2009-01-07

Revised: 2009-04-15

Published Online: 2011-01-07

Published in Print: 2011-01-01


Citation Information: Advances in Geometry, Volume 11, Issue 1, Pages 169–189, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.045.

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Citing Articles

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[1]
F. Brackx, H. De Schepper, D. Eelbode, R. Lávička, and V. Souček
Complex Variables and Elliptic Equations, 2017, Volume 62, Number 5, Page 616
[2]
Lin Chen, Guangbin Ren, and Haiyan Wang
Frontiers of Mathematics in China, 2015, Volume 10, Number 3, Page 523
[3]
F. Brackx, H. De Schepper, D. Eelbode, R. Lávička, and V. Souček
Advances in Applied Clifford Algebras, 2014, Volume 24, Number 4, Page 955
[4]
Guangbin Ren, Lin Chen, and Haiyan Wang
Complex Variables and Elliptic Equations, 2015, Volume 60, Number 3, Page 333
[5]
F. Brackx, H. De Schepper, D. Eelbode, R. Lávička, and V. Souček
Annals of Global Analysis and Geometry, 2014, Volume 46, Number 4, Page 409
[6]
Ricardo Abreu-Blaya, Juan Bory-Reyes, Fred Brackx, Hennie De Schepper, Tania Moreno-García, and Frank Sommen
Complex Analysis and Operator Theory, 2015, Volume 9, Number 5, Page 957
[7]
Ricardo Abreu-Blaya, Juan Bory-Reyes, Fred Brackx, Hennie De Schepper, and Frank Sommen
Complex Variables and Elliptic Equations, 2013, Volume 58, Number 8, Page 1057
[8]
Ricardo Abreu-Blaya, Juan Bory-Reyes, Fred Brackx, Hennie De Schepper, and Frank Sommen
Complex Analysis and Operator Theory, 2012, Volume 6, Number 5, Page 971

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