# Supercomplex structures, surface soliton equations, and quasiconformal mappings

Julian Ławrynowicz; Katarzyna Kędzia; Osamu Suzuki

Annales Polonici Mathematici (1991)

- Volume: 55, Issue: 1, page 245-268
- ISSN: 0066-2216

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topJulian Ławrynowicz, Katarzyna Kędzia, and Osamu Suzuki. "Supercomplex structures, surface soliton equations, and quasiconformal mappings." Annales Polonici Mathematici 55.1 (1991): 245-268. <http://eudml.org/doc/262309>.

@article{JulianŁawrynowicz1991,

abstract = {Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple $(^\{11\},^\{11\},^\{26\})$ is mentioned. (iii) Isospectral deformations of the Hurwitz operator of the Hurwitz pair (²,²) induce various soliton equations (Theorem 3). (iv) A special complex structure, which is called a supercomplex structure, is introduced on separable Hilbert spaces (Definition 10). A correspondence between such structures and reduction solutions of Sato’s version of Kadomtsev-Petviashvili system is established (Theorem 4). (v) The general class of quasiconformal mappings in the plane is obtained from generalized Hurwitz pairs (Theorem 5). From these results we conclude that Hurwitz pairs and triples give rise to several interesting applications.},

author = {Julian Ławrynowicz, Katarzyna Kędzia, Osamu Suzuki},

journal = {Annales Polonici Mathematici},

keywords = {Hurwitz pairs; Hurwitz triples; Hurwitz operator; Neveu-Schwarz model of superstring theory; generalized Hurwitz pairs},

language = {eng},

number = {1},

pages = {245-268},

title = {Supercomplex structures, surface soliton equations, and quasiconformal mappings},

url = {http://eudml.org/doc/262309},

volume = {55},

year = {1991},

}

TY - JOUR

AU - Julian Ławrynowicz

AU - Katarzyna Kędzia

AU - Osamu Suzuki

TI - Supercomplex structures, surface soliton equations, and quasiconformal mappings

JO - Annales Polonici Mathematici

PY - 1991

VL - 55

IS - 1

SP - 245

EP - 268

AB - Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple $(^{11},^{11},^{26})$ is mentioned. (iii) Isospectral deformations of the Hurwitz operator of the Hurwitz pair (²,²) induce various soliton equations (Theorem 3). (iv) A special complex structure, which is called a supercomplex structure, is introduced on separable Hilbert spaces (Definition 10). A correspondence between such structures and reduction solutions of Sato’s version of Kadomtsev-Petviashvili system is established (Theorem 4). (v) The general class of quasiconformal mappings in the plane is obtained from generalized Hurwitz pairs (Theorem 5). From these results we conclude that Hurwitz pairs and triples give rise to several interesting applications.

LA - eng

KW - Hurwitz pairs; Hurwitz triples; Hurwitz operator; Neveu-Schwarz model of superstring theory; generalized Hurwitz pairs

UR - http://eudml.org/doc/262309

ER -

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