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1997 | 40 | 1 | 171-184
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First order calculi with values in right-universal bimodules

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
171-184
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Institute of Theoretical Physics, University of Wrocław, Pl. Maxa Borna 9, 50-204 Wrocław, Poland
  • Centro de Investigaciones Teoricas, FESC, UNAM, Apartado Postal 95, C.P. 54700 Cuautitlán Izcalli, Estado de México
  • Facultad de Estudios Superiores, Cuautitlán, Universidad Nacional Autonoma de México, Apartado Postal 25, C.P. 54700 Cuautitlán Izcalli, Estado de México
Bibliografia
  • [1] H. C. Baehr, A. Dimakis and F. Müller-Hoissen, Differential Calculi on Commutative Algebras, J. Phys. A: Math. Gen. 28 (1995), 3197-3222, hep-th/9412069.
  • [2] N. Bourbaki, Elements of mathematics.Algebra I.Chapters 1-3, Springer-Verlag, Berlin, 1989.
  • [3] A. Borowiec, V. K. Kharchenko and Z. Oziewicz, On free differentials on associative algebra, in : Non-Associative Algebra and Its Applications, S. González (ed.), Kluwer Academic Publishers, Dordrecht 1994, ISBN 0-7923-3117-6, Mathematics and its Applications, vol. 303, 46-53, (hep-th/9312023).
  • [4] A. Borowiec and V. K. Kharchenko, Algebraic approach to calculi with partial derivatives, Siberian Advances in Mathematics 5, 2 (1995), 10-37.
  • [5] A. Borowiec and V. K. Kharchenko, Coordinate calculi on associative algebras, in : Quantum Group, Formalism and Applications, J. Lukierski, Z. Popowicz and J. Sobczyk (ed.), Polish Sci. Publ. PWN Ltd., Warszawa, 1995. ISBN 83-01-11770-2, 231-241, q-alg/9501018.
  • [6] A. Borowiec and V. K. Kharchenko, First order optimum calculi, Bull. Soc. Sci. Lett. Łódź v. 45, Ser. Recher. Deform. XIX, (1995), 75-88, q-alg/9501024.
  • [7] A. Borowiec, Cartan Pairs, Czech. J. Phys. 46, 12 (1996), 1197 (q-alg/9609011).
  • [8] J. Cuntz and D. Quillen, Algebra Extension and Nonsingularity, J. Amer. Math. Soc. 8, 2 (1995), p. 251-289.
  • [9] A. Dimakis, F. Müller-Hoissen and T. Striker, Non-commutative differential calculus and lattice gauge theory, J. Phys. A: Math. Gen. 26 (1993), 1927-1949.
  • [10] G. Maltsiniotis, Le Langage des Espaces et des Groupes Quantiques, Commun. Math. Phys. 151 (1993), 275-302.
  • [11] Yu. I. Manin, Notes on quantum groups and quantum de Rham complexes., Preprint, MPI/91-60 (1991).
  • [12] E. E. Mukhin, Yang-Baxter operators and noncommutative de Rham complexes, Russian Acad. Sci. Izv. Math. 58, 2 (1994), 108-131 (in Russian).
  • [13] R. S. Pierce, Associative algebras, Graduate Texts in Mathematics # 88, Springer-Verlag, New York, 1982.
  • [14] W. Pusz and S. Woronowicz, Twisted second quantization, Reports on Mathematical Physics 27, 2 (1989), 231-257.
  • [15] W. Pusz, Twisted canonical anticommutation relations, Reports on Mathematical Phys. 27, 3 (1989), 349-360.
  • [16] K. Schmüdgen and A. Schüler, Classification of bicovariant calculi on quantum spaces and quantum groups, C. R. Acad. Sci. Paris 316 (1993), 1155-1160.
  • [17] J. Wess and B. Zumino, Covariant differential calculus on the quantum hyperplane, Nuclear Physics 18 B (1990), 303-312, Proc. Suppl. Volume in honor of R. Stora.
  • [18] S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys. 122 (1989), 125-170.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv40z1p171bwm
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