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Document Server@UHasselt (58.026 recursos)

Repository of the University of Hasselt containing publications in the fields of statistics, computer science, information strategies and material from the Institute for behavioural sciences.

Dept. Mathematics-Physics-Informatics (WNI) - Algebra

Mostrando recursos 1 - 20 de 140

  1. Non-commutative P-1-bundles over commutative schemes

    VAN DEN BERGH, Michel
    In this paper we develop the theory of non-commutative P-1-bundles over commutative (smooth) schemes. Such non-commutative P-1-bundles occur in the theory of D-modules but our definition is more general. We can show that every non-commutative deformation of a Hirzebruch surface is given by a non-commutative P-1-bundle over P-1 in our sense.

  2. Caldararu's conjecture and Tsygan's formality

    Calaque, Damien; Rossi, Carlo A.; Van den Bergh, Michel
    In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over polyvector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet. (The existence of the latter was conjectured by Tsygan.) We also rely on the fact - recently proved by the first two authors - that Shoikhet's quasi-isomorphism is compatible with...

  3. The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven

    Ooms, Alfons
    Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S(g), including some simple criteria regarding its polynomiality, and also on certain Poisson commutative subalgebras of S(g). These facts are then used to finish our earlier work on this subject, i.e. to give an explicit description for the Poisson center of all indecomposable, nilpotent Lie algebras of dimension at most seven. Among other things, we also provide a polynomial, maximal Poisson commutative subalgebra of S(g), enjoying additional properties. As a by-product we show...

  4. Braided groups and quantum groupoids

    Liu, G. H.; Zhu, Haixing
    Let H be a quasitriangular weak Hopf algebra. It is proved that the centralizer subalgebra of its source subalgebra in H is a braided group (or Hopf algebra in the category of left H-modules), which is cocommutative and also a left braided Lie algebra in the sense of Majid.

  5. The Calabi-Yau property of smash products

    Yu, Xiaolan; Zhang, Yinhuo
    Let H be a semisimple Hopf algebra and R a braided Hopf algebra in the category of Yetter-Drinfeld modules over H. When R is a Calabi-Yau algebra, a necessary and sufficient condition for R # H to be a Calabi-Yau Hopf algebra is given. Conversely, when H is the group algebra of a finite group and the smash product R # H is a Calabi-Yau algebra, we give a necessary and sufficient condition for the algebra R to be a Calabi-Yau algebra. (C) 2012 Elsevier Inc. All rights reserved.

  6. A note on the antipode for algebraic quantum groups

    Delvaux, Lydia; Van Daele, A.; Wang, S.
    Recently, Beattie, Bulacu ,and Torrecillas proved Radford's formula for the fourth power of the antipode for a co-Frobenius Hopf algebra. In this note, we show that this formula can be proved for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). This, of course, not only includes the case of a finite-dimensional Hopf algebra, but also that of any Hopf algebra with integrals (co-Frobenius Hopf algebras). Moreover, it turns out that the proof in this more general situation, in fact, follows in a few lines from well-known formulas obtained earlier in the theory of regular multiplier Hopf algebras...

  7. Transmutation theory of a coquasitriangular weak Hopf algebra

    Liu, Guohua; Chen, Quanguo; ZHU, Haixing
    Let H be a coquasitriangular quantum groupoid. In this paper, using a suitable idempotent element e in H, we prove that eH is a braided group (or a braided Hopf algebra in the category of right H-comodules), which generalizes Majid's transmutation theory from a coquasitriangular Hopf algebra to a coquasitriangular weak Hopf algebra.

  8. Transmutation theory of a coquasitriangular weak Hopf algebra

    Liu, Guohua; Chen, Quanguo; ZHU, Haixing
    Let H be a coquasitriangular quantum groupoid. In this paper, using a suitable idempotent element e in H, we prove that eH is a braided group (or a braided Hopf algebra in the category of right H-comodules), which generalizes Majid's transmutation theory from a coquasitriangular Hopf algebra to a coquasitriangular weak Hopf algebra.

  9. Noncommutative Quadrics

    VAN DEN BERGH, Michel
    In this paper, we describe noncommutative versions of P(1) x P(1). These contain the class of noncommutative deformations of P(1) x P(1).

  10. Bicrossproducts of multiplier Hopf algebras

    DELVAUX, Lydia; Van Daele, A.; Wang, S. H.
    In this paper, we generalize Majid's bicrossproduct construction. We start with a pair (A, B) of two regular multiplier Hopf algebras. We assume that B is a right A-module algebra and that A is a left B-comodule coalgebra. The right action of A on B gives rise to the smash product A # B. The left coaction of B on A gives a possible coproduct Delta(#) on A # B. We discuss in detail the necessary compatibility conditions between the action and the coaction for Delta(#) to be a proper coproduct on A # B. The result is again a...

  11. BIFURCATIONS OF MULTIPLE RELAXATION OSCILLATIONS IN POLYNOMIAL LIENARD EQUATIONS

    DE MAESSCHALCK, Peter; DUMORTIER, Freddy
    In this paper, we prove the presence of limit cycles of given multiplicity, together with a complete unfolding, in families of (singularly perturbed) polynomial Lienard equations. The obtained limit cycles are relaxation oscillations. Both classical Lienard equations and generalized Lienard equations are treated.

  12. Deformed Calabi-Yau completions

    Keller, Bernhard; VAN DEN BERGH, Michel
    We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non-Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety. We show that deformed Calabi-Yau completions do have the Calabi-Yau property and that their construction is compatible with derived equivalences and with localizations. In particular, Ginzburg dg algebras have the Calabi-Yau property. We show that deformed 3-Calabi-Yau completions of algebras of global dimension at most 2 are quasi-isomorphic to Ginzburg...

  13. High prevalence of F4(+) and F18(+) Escherichia coli in Cuban piggeries as determined by serological survey

    de la Fe Rodriguez, Pedro Yoelvys; Coddens, Annelies; DEL FAVA, Emanuele; CORTINAS ABRAHANTES, Jose; SHKEDY, Ziv; Maroto Martin, Luis O.; Cruz Munoz, Eduardo; DUCHATEAU, Luc; Cox, Eric; Goddeeris, Bruno Maria
    Little information is available on the prevalence of swine enteropathogens in Cuba where diarrheic diseases are responsible for 31% and 37% of the total mortality during the neonatal and postweaning periods. F4(+) and F18(+) enterotoxigenic Escherichia coli and F18(+) verotoxigenic E. coli induce diarrhea and edematous disease in pigs, but their distribution has never been thoroughly studied in the Cuban swine population. Therefore, the present study estimated the prevalence of F4- and F18-specific antibodies in sera of 1,044 6-month-old gilts distributed in 34 piggeries spread over the Cuban territory. For the data analysis, which included the optical density of individual...

  14. On two examples by Iyama and Yoshino

    Keller, Bernhard; Murfet, Daniel; VAN DEN BERGH, Michel
    In a recent paper, Iyama and Yoshino considered two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper, we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov's result on the graded singularity category.

  15. Hopf algebra actions on differential graded algebras and applications

    He, Ji-Wei; Van Oystaeyen, Fred; ZHANG, Yinhuo
    Let H be a finite dimensional semisimple Hopf algebra, A a differential graded (dg for short) H-module algebra. Then the smash product algebra A#H is a dg algebra. For any dg A#H-module M, there is a quasi-isomorphism of dg algebras: RHom(A) (M, M)#H -> RHom(A#H)(M circle times H, M circle times H). This result is applied to d-Koszul algebras, Calabi-Yau algebras and AS-Gorenstein dg algebras.

  16. ALGEBRAIC QUANTUM HYPERGROUPS II. CONSTRUCTIONS AND EXAMPLES

    DELVAUX, Lydia; Van Daele, A.
    Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct Delta on A making the pair (A, Delta) a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic quantum group as introduced and studied in [A. Van Daele, Adv. Math. 140 (1998) 323]. Now let H be a finite subgroup of G and consider the subalgebra A(1) of functions in A that are constant on double cosets of H. The coproduct in general will not leave this algebra...

  17. Algebraic quantum hypergroups

    DELVAUX, Lydia; Van Daele, A.
    An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is characterized in terms of these integrals. We construct the dual, just as in the case of algebraic quantum groups and we show that the dual of the dual is the original quantum...

  18. Abelian 1-Calabi-Yau Categories

    VAN ROOSMALEN, Adam-Christiaan
    In this paper, we show all k-linear abelian 1-Calabi-Yau categories over an algebraically closed field k are derived equivalent to either the category of coherent sheaves on an elliptic curve, or to the finite dimensional representations of k[[t]]. Since all abelian categories derived equivalent with these two are known, we obtain a classification of all k-linear abelian 1-Calabi-Yau categories up to equivalence.

  19. Cocommutative Calabi-Yau Hopf algebras and deformations

    He, Ji-Wei; Van Oystaeyen, Fred; ZHANG, Yinhuo
    The Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS-Gorenstein Hopf algebras. It is shown that the skew-group algebra of a universal enveloping algebra of a finite dimensional Lie algebra g with a finite subgroup G of automorphisms of g is Calabi-Yau if and only if the universal enveloping algebra itself is Calabi-Yau and G is a subgroup of the special linear group SL(g). The Noetherian cocommutative Calabi-Yau Hopi algebras of dimension not larger than 3 are described. The Calabi-Yau property of Sridharan enveloping algebras of finite...

  20. DERIVED H-MODULE ENDOMORPHISM RINGS

    He, Ji-Wei; Van Oystaeyen, Fred; ZHANG, Yinhuo
    Let H be a Hopf algebra, A/B be an H-Galois extension. Let D(A) and D(B) be the derived categories of right A-modules and of right B-modules, respectively. An object M-. is an element of D(A) may be regarded as an object in D(B) via the restriction functor. We discuss the relations of the derived endomorphism rings E-A(M-.) =. circle plus i is an element of zHom(D(A))(M-. , M-. [i]) and E-B(M-.) = circle plus i is an element of z Hom(D(B))(M-., M-. [i]). If H is a finite-dimensional semi-simple Hopf algebra, then E-A(M-.) is a graded sub-algebra of E-B(M-.). In...

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