Margaret Beattie

Professor emeritus

Margaret Beattie

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I first joined the Mount Allison faculty in 1982 and retired from teaching in 2012.  My most recent publication appeared in 2014 -- see List of Publications below. 


MSc. Queen's University, 1971

PhD Queen's University, 1977

Research interests

My mathematical research is in Pure Mathematics, specifically in Algebra, and, more specifically, in Ring Theory.  I am interested in the algebraic structure of Hopf algebras, including quantum groups, and in their actions and coactions on rings.  This includes graded rings and modules.  In recent years I have been working on the classification of low dimensional Hopf algebras over the complex numbers. 








  1. Menini, Claudia; Ardizzoni, Alessandro; Beattie, Margaret  Quantum lines for dual quasi-bialgebras, Algebr. Represent. Theory, 2014
  2. Beattie, Margaret; García, Gastón Andrés Techniques for classifying Hopf algebras and applications to dimension p3 . Comm. Algebra 41 (2013), no.8, 3108-3129.
  3. Beattie, Margaret; García, Gastón Andrés Classifying Hopf algebras of a given dimension. Hopf algebras and tensor categories, 125-152, Contemp. Math., 585, Amer. Math. Soc., Providence, RI, 2013.
  4. Ardizzoni, Alessandro; Beattie, Margaret; Menini, Claudia   Gauge deformations for Hopf algebras with the dual Chevalley property.  J. Algebra Appl. 11(2012), no. 3.  
  5. Beattie, Margaret; Caenepeel, Stefaan; Raianu, Şerban  Stable equivalence of Morita type and Frobenius extensions. Ann. Univ.Buchar. Math. Ser. 2(LX) (2011), no.2, 123-126.
  6. Ardizzoni, Alessandro; Beattie, Margaret; Menini, Claudia  Cocycle deformations for liftings of quantum linear spaces.  Comm. Algebra 39 (2011) no. 12, 4518-4535.
  7. Ardizzoni, Alessandro; Beattie, Margaret; Menini, Claudia Cocycle deformations for Hopf algebras with a coalgebra projection.  J. Algebra 324 (2010), no. 4, 673-705.
  8. Beattie, Margaret; Bulacu, Daniel  On the antipode of a co-Frobenius (co)quasitriangular Hopf algebra.  Comm. Algebra 37(2009), no. 9, 2981-2993.
  9. Beattie, Margaret A survey of Hopf algebras of low dimension. Acta Appl. Math. 108(2009), no.1, 19-31.
  10. Beattie, M.; Iovanov, M.C.; Raianu, Ş.  The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective.  Algebr. Represent. Theory 12 (2009), no.2-5, 251-255.  
  11. Beattie, M.; Bulacu, D.; Raianu, Ş.  Balanced bilinear forms for corings.  Modules and comodules, 87-99, Trends Math., Birkhäuser Verlag, Basel, 2008.
  12. Beattie, Margaret; Bulacu, Daniel  Braided Hopf algebras obtained from coquasitriangular Hopf algebras, Comm. Math. Phys. 282 (2008), no.1, 115-160.
  13. Beattie, M.; Rose, R.  Balanced bilinear forms on matrix and matrix-like coalgebras, Comm. Algebra 36 (2008), no.4, 1311-1319.
  14. Beattie, Margaret; Bulacu, Daniel; Torrecillas, Blas Radford's S4 formula for co-Frobenius Hopf algebras.  J. Algebra 307 (2007), no. 1,330-342.  
  15. Beattie, M.; Weatherby, C. Student Research Project: Integer points on a hyperboloid of one sheet.  The College Mathematics Journal, Vol. 37, No.1, January 2006.
  16. Beattie, M.; Weatherby, C.  Pythagorean triples and units of integral group rings , J. Algebra Appl. 4 (2005), no.4, 355-367.
  17. Andruskiewitsch, N; Beattie, M.  Irreducible representations of liftings of quantum planes, Lie theory and its applications in physics V, 414-423, World Sci. Publ., River Edge, NJ, 2004.
  18. Andruskiewitsch, N; Beattie, M. The coradical of the dual of a lifting of a quantum plane. Hopf algebras, 47-63, Lecture Notes in Pure and Appl. Math., 237, Dekker, New York, 2004.
  19. Beattie, M;  Dăscălescu, S. Hopf algebras of dimension 14.  J.London Math. Soc (2) 69 (2004), no.1, 65-78.  
  20. Beattie, M. Duals of pointed Hopf algebras. J. Algebra 262 (2003), no. 1, 54-76  
  21. Beattie, M. Corrigendum to: "Duals of pointed Hopf algebras" [J. Algebra 262 (2003), no. 1, 54-76] J. Algebra 320 (2008), no. 10, 3849.
  22. Beattie, M.;  Dăscălescu, S.; Raianu, Ş.  Lifting of Nichols algebras of type B2. With an appendix by the authors and Ian Rutherford. Israel J. Math. 132(2002), 1-28.  
  23. Beattie, M.;  Dăscălescu, S.; Raianu, Ş. A co-Frobenius Hopf algebra with a separable Galois extension is finite. Proc. Amer. Math. Soc. 128. (2000), no 11, 3201-3203.
  24. Beattie, Margaret; Torrecillas, Blas  Twistings and Hopf Galois extensions. J. Algebra 232 (2000), no.2 p 673-696.
  25. Beattie, M.;  Dăscălescu, S.; Grünenfelder, L.  Constructing pointed Hopf algebras by Ore extensions, J. Algebra 225(2000), no.2, 743-770. 
  26. Beattie, M.;  Dăscălescu, S.; Grünenfelder, L.  On pointed Hopf algebras of dimension pn. Proc. Amer. Math. Soc. 128 (2000), no.2, 361-367. 
  27. Beattie, M.  An isomorphism theorem for Ore extension Hopf algebras.  Comm. Algebra 28 (2000), no.2, 569-584.
  28. Beattie, M.;  Dăscălescu, S.; Grünenfelder, L. On the number of types of finite-dimensional Hopf algebras.  Invent. Math. 136(1999), no. 1, 1-7.
  29. Beattie, Margaret; del Río,  Ángel  Graded equivalences and Picard groups.  J. Pure Appl. Algebra 141 (1999), no.2, 131-152
  30. Beattie, M.;  Dăscălescu, S.; Raianu, Ş.; Van Oystaeyen, F.   The categories of Yetter-Drinfel'd modules, Doi-Hopf modules and two-sided two-cosided Hopf modules.  Appl. Categ. Structures 6(1998), no.2, 223-237.
  31. Beattie, M.;  Dăscălescu, S.; Grünenfelder, L.; Năstăsescu, C.  Finiteness conditions, co-Frobenius Hopf algebras and quantum groups. J. Algebra 200 (1998), no.1,312-333.
  32. Beattie, M.;  Dăscălescu, S.; Raianu, Ş.  Galois extensions for co-Frobenius Hopf algebras. J. Algebra 198(1997), no.1, 164-183.
  33. Beattie, M. ; Chen, C.-Y.; Zhang, J.J.  Twisted Hopf comodule algebras. Comm. Algebra 24 (1996), no.5, 1759-1775.
  34. Beattie, Margaret; del Río,  Ángel   The Picard group of a category of graded modules.  Comm. Algebra 24 (1996), no.14, 4397-4414.
  35. Beattie, M.;  Dăscălescu, S. Categories of modules graded by G-sets. Applications. Contact Franco-Belge en Algèbre (Diepenbeek, 1993).  J. Pure Appl. Algebra 107 (1996), no.2, 129-139.
  36. Beattie, M.;  Dăscălescu, S.; Năstăsescu, C.  A note on semilocal graded rings.  Rev. Roumaine Math. Pures Appl. 40 (1995), no.3-4, 253-258.
  37. Beattie, M.  Cocycles and right crossed products.  Rings, extensions, and cohomology (Evanston, Il, 1993), 19-29, Lecture Notes in Pure and Appl. Math., 150, Dekker, New York, 1994. 
  38. Beattie, Margaret A right crossed product and duality.  Comm. Algebra 22 (1994), no.1, 229-241.
  39. Beattie, M. Smash products for right comodule algebras. Proceedings of the First China-Japan International Symposium on Ring Theory (Guilin, 1991), 11-13, Okayama Univ., Okayama, 1992.
  40. Beattie, Margaret Strongly inner actions, coactions, and duality theorems.  Tsukuba J. Math. 16 (1992), no.2, 279-293.
  41. Beattie, Margaret; Orzech, Morris  Prime ideals and finiteness conditions for Gabriel topologies over commutative rings.  Rocky Mountain J. Math. 22 (1992), no.2, 423-439.
  42. Beattie, Margaret  On the Blattner-Montgomery duality theorem for Hopf algebras.  Azumaya algebras, actions, and modules (Bloomington, IN, 1990), 23-28, Comtemp. Math., 124, Amer. Math. Soc. Providence, RI, 1992.
  43. Beattie, M.; Stewart, P.  Graded radicals of graded rings.  Acta Math. Hungar. 58 (1991), no.3-4, 261-272.
  44. Liu, Shao Xue; Beattie, Margaret; Fang, Hong Jin  Graded division rings and the Jacobson density theorem.  Beijing Shifan Daxue Xuebao 27 (1991), no.2,  129-134. 
  45. Beattie, Margaret; Jespers, Eric  On perfect graded rings.  Comm. Algebra 19 (1991), no.8, 2363-2371.
  46. Beattie, M.A.; Liu, S.-X.; Stewart, P.N.  Comparing graded versions of the prime radical.  Canad. Math. Bull. 34 (1991), no. 2, 158-164.
  47. Caenepeel, S.; Beattie, M.  A cohomological approach to the Brauer-Long group and the groups of Galois extensions and strongly graded rings. Trans. Amer. Math. Soc. 324 (1991), no. 2, 747-775. 
  48. Beattie, Margaret; Ulbrich, K.-H.  A Skolem-Noether theorem for Hopf algebra actions.   Comm. Algebra 18 (1990), no. 11, 3713-3724.
  49. Beattie, Margaret; Stewart, Patrick  Graded versions of radicals.  Algebra and geometry (Santiago de Compostela, 1989), 71-22, Álxebra, 54, Univ. Santiago de Compostela, Santiago de Compostela, 1990.
  50. Beattie, M.; Caenepeel, S.  The Brauer-Long group of Z/ptZ-dimodule algebras.  J. Pure Appl. Algebra 60 (1989), no.3, 210-236.
  51. Beattie, Margaret  Inner gradings and Galois extensions with normal basis.  Proc. Amer. Math. Soc. 107 (1989), no. 4, 881-886.
  52. Beattie, Margaret Duality theorems for group actions and gradings.  Ring theory (Granada, 1986), 28-32, Lecture Notes in Math., 1328, Springer, Berlin, 1988.
  53. Beattie, Margaret A generalization of the smash product of a graded ring.  J. Pure Appl. Algebra 52 (1988), no. 3, 219-226.
  54. Beattie, Margaret Duality theorems for rings with actions or coactions. J. Algebra 115 (1988), no.2, 303-312.
  55. Beattie, Margaret The subgroup structure of the Brauer group of RG-dimodule algebras. Ring theory (Antwerp, 1985), 20-30, Lecture Notes in Math., 1197, Springer, Berlin, 1986.
  56. Beattie, Margaret Computing the Brauer group of graded Azumaya algebras from its subgroups, J. Algebra 101 (1986), no.2, 339-349.
  57. Beattie, Margaret Automorphisms of G-Azumaya algebras.  Canad. J. Math. 37 (1985), no. 6, 1047-1058.
  58. Beattie, Margaret The Brauer group of central separable G-Azumaya algebras. J. Algebra 54 (1978), no.2, 516-525.
  59. Beattie, Margaret A direct sum decomposition for the Brauer group of H-module algebras, J. Algebra 43 (1976), no. 2, 686-693.