PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 40 | 1 | 79-90
Tytuł artykułu

Bicovariant differential calculi and cross products on braided Hopf algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In a braided monoidal category C we consider Hopf bimodules and crossed modules over a braided Hopf algebra H. We show that both categories are equivalent. It is discussed that the category of Hopf bimodule bialgebras coincides up to isomorphism with the category of bialgebra projections over H. Using these results we generalize the Radford-Majid criterion and show that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. In specific braided monoidal abelian categories we define (bicovariant) braided differential calculi over H and apply the results on Hopf bimodules to construct a higher order bicovariant differential calculus over H out of any first order bicovariant differential calculus over H. This object is shown to be a bialgebra with universal properties.
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
79-90
Opis fizyczny
Daty
wydano
1997
Twórcy
  • National Academy of Sciences, Bogolyubov Institute for Theoretical Physics, 252 143, Kiev-143, Ukraine
  • Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven-Heverlee, Belgium
Bibliografia
  • [1] Yu. Bespalov, Crossed Modules and Quantum Groups in Braided Categories, to appear in Appl. Categorical Structures.
  • [2] Yu. Bespalov and B. Drabant, Hopf (Bi-)Modules and Crossed Modules in Braided Monoidal Categories, preprint UVA-FWI 95-18 (1995).
  • [3] Yu. Bespalov and B. Drabant, Differential Calculus in Braided Abelian Categories, in preparation.
  • [4] T. Brzezinski, Remarks on Bicovariant Differential Calculi and Exterior Hopf Algebras, Lett. Math. Phys. 27, 287 (1993).
  • [5] B. Drabant, Braided Bosonization and Inhomogeneous Quantum Groups, Preprint UVA-FWI 94-28 (1994), to appear in Acta Math. Appl.
  • [6] P. Freyd and D. Yetter, Braided compact closed categories with applications to low dimensional topology, Adv. Math. 77, 156 (1989).
  • [7] D. Husemoller, Cyclic Homology, Tata Institute Lecture Notes on Mathematics 83, Springer (1991).
  • [8] A.P. Isaev and A.A. Vladimirov, $GL_q(n)$-Covariant Braided Differential Bialgebras, Lett. Math. Phys. 33, 297 (1995).
  • [9] A. Joyal and R. Street, Braided monoidal categories, Mathematics Reports 86008, Macquarie University (1986).
  • [10] S. Majid, Algebras and Hopf algebras in braided categories, Advances in Hopf Algebras, Lecture Notes in Pure and Appl. Math. 158, 55, Dekker (1994).
  • [11] S. Majid, Cross Products by Braided Groups and Bosonization, J. Algebra 163, 165 (1994).
  • [12] S. Majid, Transmutation theory and rank for quantum braided groups, Math. Proc. Camb. Phil. Soc. 113, 45 (1993).
  • [13] S. Majid, Free Braided Differential Operators, Braided Binomial Theorem, and the Braided Exponential Map, J. Math. Phys. 34, 4843 (1993).
  • [14] S. Mac Lane, Categories. For the Working Mathematician, GTM 5, Springer (1972).
  • [15] S. Mac Lane, Natural associativity and commutativity, Rice University Studies 49, 28 (1963).
  • [16] Yu. I. Manin, Notes on Quantum Groups and Quantum de Rham Complexes, J. Theor. and Math. Phys. 92, 425 (1992). G. Maltsiniotis, Le langage des espaces et des groupes quantiques, Commun. Math. Phys. 151, 275 (1993).
  • [17] D.E. Radford, The Structure of Hopf Algebras with a Projection, J. Algebra 92, 322 (1985).
  • [18] D.E. Radford and J. Towber, Yetter-Drinfel'd categories associated to an arbitrary bialgebra, J. Pure Appl. Algebra 87, 259 (1993).
  • [19] M.E. Sweedler, Hopf algebras, W.A. Benjamin, New York (1969).
  • [20] S.L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups), Commun. Math. Phys. 122, 125 (1989).
  • [21] D. Yetter, Quantum groups and representations of monoidal categories, Math. Proc. Camb. Phil. Soc. 108, 261 (1990).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv40z1p79bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.