Abstract
The present paper gives a specification of the general duality theorem due — in the case of Hurwitz pairs — to Ławrynowicz, Porter, Ramirez de Arellano and Rembieliński (1989), and — in the case of J 3-triples — to Adem, Ławrynowicz and Rembieliński (1990). The specification, obtained by an independent method, based upon the duality Theorem 2 due to Furuoya, Kanemaki, Ławrynowicz and Suzuki (1993), visualizes a remarkable duality between the Kaluza-Klein and Penrose theories. In the lowest-dimensional case it refers to the Hurwitz pairs of bidimension (8,5).
Research supported by the Grant PB 2 1140 91 01.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adern, J., Ławrynowicz, J., and Rembieliński, J. (1990) ‘Generalized Hurwitz maps of the type S × V → W’ Dep. de Mat. Centro de Investigación y de Estudios Avanzados México Preprint no. 80, ii + 20 pp.
Delanghe, R., Sommen, F., and Souček, V. (1992) Clifford Algebra and Spinor-Valued Functions. A Function Theory for the Dirac Operator (Series: Mathematics and Its Applications 53), Kluwer Academic Publ., Dordrecht-Boston-London, xviii + 485 pp.
Furuoya, I., Kanemaki, S., Ławrynowicz, J., and Suzuki, O. (1993) ‘Hermitian Hurwitz pairs’, this volume, pp. 137–154.
Kanemaki, S., and Suzuki, O. (1989) ‘Hermitian pre-Hurwitz pairs and the Minkowski space’, in J. Ławrynowicz (ed.), Deformations of Mathematical Structures. Complex Analysis with Physical Applications. Selected papers from the Seminar on Deformations, Łódź-Lublin 1985/87, Kluwer Academic Publ., Dordrecht-Boston-London, pp. 225–232.
Ławrynowicz, J. (1993) ‘Clifford Analysis and the five-dimensional analogues of the quaternionic structure of the Kałuża-Klein and Penrose types’, Ber. Univ. Jyväskylä Math. Inst. 55, 97–112.
Ławrynowicz, J. (1993) ‘Quantized complex and Clifford structures’, Ber. Univ. Jyväskylä Math. Inst. 55, 113–120.
Ławrynowicz, J., Koshi, S., and Suzuki, O. (1993) ‘Dualities generated by the generalised Hurwitz problem and variation of the Yang-Mills field’, to appear.
Ławrynowicz, J. and Kovacheva, R. (1991) ‘Quasiregular extension and approximation of dualities generated by the generalized Hurwitz problem’, in R. Kühnau and W. Tutschke (eds.), Geometric Function Theory and Applications II, Longman Scientific and Technical, Harlow-London-New York, pp. 100–117.
Ławrynowicz, J., Porter, R.M., Ramírez de Arellano, E., and Rembieliński, J. (1992) ‘On the dualities generated by the generalised Hurwitz problem’, this volume, pp. 189–208.
Ławrynowicz, J. and Rembieliński, J. (1985) ‘Supercomplex vector spaces and spontaneous symmetry breaking’, in S. Coen (ed.), Seminari di Geometria 1984, Università di Bologna, Bologna, pp. 131–154.
Ławrynowicz, J. and Rembieliński, J. (1987) ‘Pseudo-euclidean Hurwitz pairs and the Kałuza-Klein theories’, J. Phys. A: Math. Gen. 20, 5831–5848.
Ławrynowicz, J. and Rembieliński, J. (1989) ‘On the composition of nondegenerate quadratic forms with an arbitrary index’, Ann. Fac. Sci. Toulouse Math. (5) 10, 141–168.
Ławrynowicz, J. and Wojtczak, L., in cooperation with Koshi, S. and Suzuki, O. (1993) ‘Stochastical mechanics of particle systems in Clifford-analytical formulation related to Hurwitz pairs of bidimension (8,5)’, this volume, pp. 213–262.
Manin, Yu.I. (1988) Gauge Field Theory and Complex Geometry (Grundlehren der mathematischen Wissenschaften 289), Springer-Verlag, Berlin-Heideiberg-New York-Paris-Tokyo [trans], from Russian].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Ławrynowicz, J., Suzuki, O. (1994). The Duality Theorem for the Hurwitz Pairs of Bidimension (8,5) and the Penrose Theory. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1896-5_9
Download citation
DOI: https://doi.org/10.1007/978-94-011-1896-5_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4838-5
Online ISBN: 978-94-011-1896-5
eBook Packages: Springer Book Archive