M. Beattie - Publications since 1994

  • A. Ardizzoni, M. Beattie and C. Menini, Cocycle deformations for Hopf algebras with a coalgebra projection, J. Algebra, 324 (2010), 673-705.

  • M. Beattie, A survey of Hopf algebras of low dimension, Proceedings of “Groups, rings, Lie and Hopf algebras “, 2007, Bonne Bay, Nfld, Acta Applicandae Mathematicae, 108 No.1 (2009), 19-31.

  • M. Beattie, M.C.Iovanov, S. Raianu, The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective, Algebr. Represent. Theor. 12 (2009), 251-255. Preprint posted on the Mathematics ArXiv .

  • M. Beattie, D. Bulacu and S. Raianu, Balanced bilinear forms for corings, in "Modules and Comodules", Trends in Mathematics, 87-99, Birkhauser Verlag, 2008. Available as a pdf file .

  • M. Beattie and D. Bulacu, On the antipode of a coFrobenius (co)quasitriangular Hopf algebra, , Communications in Algebra 37 (2009), 1-13; posted on the Mathematics ArXiv

  • M. Beattie and R. Rose, Balanced bilinear forms on matrix and matrix-like coalgebras, Communications in Algebra 36 (2008) 1311-1319. preprint in pdf format.

  • Margaret Beattie and Daniel Bulacu, Braided Hopf algebras obtained from coquasitriangular Hopf algebras, Commun. Math. Phys. 282 (2008), 115-160. Posted on the Mathematics ArXiv

  • Margaret Beattie, Daniel Bulacu, Blas Torrecillas, Radford's S^4 formula for co-Frobenius Hopf algebras, J. Algebra 307 (2007), 330-342. Preprint is posted on Mathematics ArXiv ,

    The interested reader might also like to consult
    (for weak Hopf algebras) Peter Vecsernyes, Larson-Sweedler theorem and the role of grouplike elements in weak Hopf algebras, J. Alg. 270 (2003), 471-520
    (for multplier Hopf algebras) L. Delvaux, A. Van Daele, Shuanhong Wang, A note on Radford's S^4 formula, Mathematics ArXiv
    (for biFrobenius algebras) Walter Ferrar Santos and Mariana Haim, Radford's formula for biFrobenius algebras and applications, Mathematics ArXiv

  • M. Beattie and C. Weatherby, Student Research Project: Integer Points on a Hyperboloid of One Sheet, The College Mathematics Journal, Vol. 37, No 1, January 2006.

  • M. Beattie and C. Weatherby, Pythagorean triples and units of integral group rings , Journal of Algebra and its Applications, Vol.4, No.4, 2005, 355-367.
    A preprint form is available in pdf format.

  • N. Andruskiewitsch and M. Beattie, Irreducible representations of liftings of quantum planes, in "Lie Theory and its Applications in Physics V", Proceedings of the Fifth International Workshop, Varna, Bulgaria, 2003, Edit. H-D Doebner & V K Dobrev, World Scientific, 2004.
    This paper is available at Mathematics arXiv.

  • N. Andruskiewitsch and M. Beattie, The coradical of the dual of a lifting of a quantum plane, in "Hopf algebras", edited by J. Bergen, S. Catoiu, W. Chin, Proceedings of the International Conference on Hopf algebras and quantum groups, DePaul Univ., 2004, 47-63.
    A preprint form is available in pdf format.

  • M. Beattie, S. D\u{a}sc\u{a}lescu, Hopf algebras of dimension 14, J.London Math. Soc (2004), 1-14. Mathematics ArXiv QA/0205243

  • Margaret Beattie, Sorin D\u{a}sc\u{a}lescu, Serban Raianu, Lifting of Nichols Algebras of Type $B_2$, with an Appendix: A generalization of the q-binomial theorem. Appendix with Ian Rutherford ,Isreal J. Math.(2002), 1-28, Mathematics ArXiv QA/0204075

  • M. Beattie, Duals of pointed Hopf algebras , Journal of Algebra, Volume 262, Issue 1, 1 April 2003, Pages 54-76 Mathematics ArXiv QA/0202091

  • M. Beattie, S. Dascalescu and S. Raianu , A co-Frobenius Hopf algebra with a separable Galois extension is finite.
    Proc. Amer. Math. Soc. 128. No 11, 3201-3203.
    Abstract: If H is a co-Frobenius Hopf algebra over a field, having a Galois H-object A which is separable over AcoH, its ring of coinvariants, then H is finite-dimensional.
    A preprint form is available in dvi format.

  • Margaret Beattie and Blas Torrecillas, Twistings and Hopf Galois extensions J. Algebra 232 (2000)nr.2 p 673-696
    Abstract: Let k be a commutative ring, H a k-Hopf algebra, and A a right H-comodule algebra. A twisting of A is a map \tau: H \otimes A \to A such that (A,*_{\tau}, \rho_A) is also an H-comodule algebra , where the product *_{\tau} is defined by a*_{\tau}b = \sum a_0 \tau(a_1 \otimes b). In this note, we observe that there is a map of pointed sets from the twistings of A to the H-measurings from AcoH to A and study the set of twistings that map to the trivial measuring. If A/AcoH is Galois and H is finitely generated projective, then the twistings that map to the trivial measuring can be described as a set of invertible twisted cocycles \varphi: H \otimes H \to A. An equivalence relation on the set of twisted cocycles corresponds to isomorphism classes of Galois extensions.
    A preprint version is available in dvi format.

  • M. Beattie, S. Dascalescu, L. Grunenfelder, Constructing pointed Hopf algebras by Ore extensions, J. Algebra 225(2000) nr.2 p.743-770
    Abstract: We present a general construction producing pointed co-Frobenius Hopf algebras and give some classification results for the examples obtained.
    A preprint version is available in dvi format.

  • M. Beattie, An isomorphism theorem for Ore extension Hopf algebras, Communications in Algebra 28(2) (2000), p.569-584.
    Abstract: A complete description of isomorphisms between Ore extension Hopf algebras is given and used to enumerate all Ore extension Hopf algebras H with the order of G(H) equal to 4 and skew-primitives with square in H0.
    A preprint version is available in dvi format.

  • M. Beattie, S. Dascalescu, L. Grunenfelder, On pointed Hopf algebras of dimension pn, Proc. Amer. Math. Soc. 128 (1999), 361-367.
    Abstract: In this note we describe non-semisimple Hopf algebras of dimension pn with coradical isomorphic to kC, C abelian of order pn-1, over an algebraically closed field k of characteristic zero. If C is cyclic or C = (Cp)n-1 then we also determine the number of isomorphism classes of such Hopf algebras.
    A preprint version is available in dvi format.

  • M. Beattie, S. Dascalescu, L. Grunenfelder, On the number of types of finite dimensional Hopf algebras , Inventiones Mathematicae 136 (1999), p.1-7.
    Abstract: For an odd prime p we construct an infinite class of non-isomorphic Hopf algebras of dimension p4 over an infinite field containing primitive p-th roots of unity, answering in the negative a long standing conjecture of Kaplansky.
    A preprint version is available in dvi format.

  • M. Beattie and Ángel del Río, Graded equivalences and Picard groups, Journal of Pure and Applied Algebra 141 (1999) p.131-152
    Abstract: We study two subgroups of the Picard group Pic(R-gr) of a category of graded modules: the subgroup gr-Pic(R#P_G) of classes of graded equivalences and the subgroup Pic(R#P_G)G of classes of equivalences which commute with the suspensions in Pic(R-gr). We prove that in general these groups are not the same and show that they are related by an exact sequence of cohomology.
    A preprint version is available in dvi format. Some related papers are posted on the web page for ring theory preprints from Spanish universities.

  • M. Beattie, S. D\u{a}sc\u{a}lescu, S. Raianu and F. Van Oystaeyen, Crossed modules and two-sided two co-sided Hopf modules, Appl. Categorical Structures 6(1998), 223-237.

  • M. Beattie, S. D\u{a}sc\u{a}lescu, L. Gr\"{u}nenfelder and C. N\u{a}st\u{a}sescu, Finiteness conditions, co-Frobenius Hopf algebras and quantum groups, J. Algebra 200 (1998), 312-333.

  • M. Beattie, S. D\u{a}sc\u{a}lescu and S. Raianu, Galois extensions for co-Frobenius Hopf algebras, J. Algebra 198(1997),164-183.

  • M. Beattie, C. Y. Chen and J. J. Zhang, Twisted Hopf comodule algebras, Comm. Alg. 24 (1996), 1759-1775.

  • M. Beattie and A. del Río, The Picard group of a category of graded modules, Comm. Alg. 24 (1996), 4397-4414.

  • M. Beattie and S. D\u{a}sc\u{a}lescu, Categories of modules graded by G-sets. Applications. J. Pure & Appl. Alg. 107 (1996), 129-139.

  • M. Beattie, S. D\u{a}sc\u{a}lescu and C. N\u{a}st\u{a}sescu, Graded semilocal rings, Rev. Romaine Math. Pures Appl. 40 (1995), 253-258.

  • M. Beattie, Cocycles and right crossed products, in `Rings, Extensions, and Cohomology', Proceedings of conference in honour of D. Zelinsky, Marcel Dekker, 1994, 19-29.

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