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## Banach Center Publications

1996 | 37 | 1 | 223-240
Tytuł artykułu

### Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of a $J^3$-triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then the interrelation with quantum groups and related Clifford-type structures is indicated via anti-involutions which also play a central role in the theory of symmetric complex manifolds. Finally, the theory is linked with a natural generalization of general linear inhomogeneous groups as quantum braided groups. This generalization is in the spirit of the theory initiated and developed by S. Majid, however, our construction differs in the interrelation between the homogeneous and inhomogeneous parts of the group. In order to study the quantum braided orthogonal groups, we consider a kind of quantum geometry in the covector space. This enables us to investigate a quantum braided Clifford algebra structure related to the spinor representation of that group.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
223-240
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
• Institute of Mathematics, Polish Academy of Sciences, Narutowicza 56, PL-90-136 Łódź, Poland
autor
• Chair of Theoretical Physics, University of Łódź, Pomorska 149/153, PL-90-236 Łódź, Poland
autor
• Dipartimento di Matematica "Guido Castelnuovo", Università di Roma I "La Sapienza", Piazzale Aldo Moro, 2, I-00-185 Roma, Italia
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