Publications of Martin Lorenz



Books and Lecture Notes

Gelfand-Kirillov Dimension and Poincaré Series

Cuadernos de Algebra, No. 7,
Universidad de Granada, 68 pp., 1988.

PDF file

Multiplicative Invariant Theory

Encyclopaedia of Mathematical Sciences, Vol. 135,
subseries "Invariant Theory and Algebraic Transformation Groups",
xii+177 pp., Springer-Verlag, 2005. ISBN 3-540-24323-2

Table of contents       Corrections and updates

A Tour of Representation Theory

Graduate Studies in Mathematics, Vol. 193, xviii+654 pp.,
American Mathematical Society, 2018

Table of contents       Corrections and updates

Articles

  1. Primitive ideals of group algebras of supersoluble groups. Math. Annalen 225, 115-122 (1977).

  2. Completely prime primitive ideals in group algebras of finitely generated nilpotent-by-finite groups. Comm. in Algebra 6, 717-734 (1978).

  3. Primitive ideals in crossed products and rings with finite group actions. Math. Zeitschr. 158, 285-294 (1978).

  4. (with D. S. Passman) Centers and prime ideals in group algebras of polycyclic-by-finite groups. J. Algebra 57, 355-386 (1979).

  5. The heart of prime ideals in Ore extensions. Manuscripta math. 28, 293-304 (1979).

  6. Analogs of Clifford's theorem for polycyclic-by-finite groups. Trans. Amer. Math. Soc. 254, 295-317 (1979).

  7. (with G. Michler) On maximal ideals in Ore extensions. In: Ring Theory, Proceedings of the 1978 Antwerp Conference, pp. 139-151. Marcel Dekker, New York, 1979.

  8. (with D. S. Passman) Prime ideals in crossed products of finite groups. Israel J. Math. 33, 89-132 (1979).

  9. (with D. S. Passman) Integrality and normalizing extensions of rings. J. Algebra 61, 289-297 (1979).

  10. (with D. S. Passman) Observations on crossed products and fixed rings. Comm. in Algebra 8, 743-779 (1980).

  11. (with D. S. Passman) Prime ideals in group algebras of polycyclic-by-finite groups. Proc. London Math. Soc. (3) 43, 520-543 (1981).

  12. (with D. S. Passman) Two applications of Maschke's theorem. Comm. in Algebra 8, 1853-1866 (1980).

  13. (with D. S. Passman) Addendum-Prime ideals in crossed products of finite groups. Israel J. Math. 35, 311-322 (1980).

  14. Finite normalizing extensions of rings. Math. Zeitschr. 176, 447-484 (1981).

  15. Prime ideals in group algebras of polycyclic-by-finite groups: Vertices and sources. In: Séminaire d'algèbre P. Dubreil et M. P. Malliavin, Lect. Notes in Mathematics No. 867, pp. 406-420, Springer, Berlin-Heidelberg-New York, 1981.

  16. Completely prime ideals in Ore extensions. Comm. in Algebra 9, 1227-1232 (1981).

  17. Chains of prime ideals in enveloping algebras of solvable Lie algebras. J. London Math. Soc. (2) 24, 205-210 (1981).

  18. (with S. Montgomery and L. W. Small) Prime ideals in fixed rings II. Comm. in Algebra 10, 449-455 (1982).

  19. (with L. W. Small) On the Gelfand-Kirillov dimension of Noetherian PI-algebras. In: Amitsur, Saltman, Seligman (eds.), Algebraists' Homage: Papers in Ring Theory and Related Topics, Contemporary Mathematics 13, 199-205 (1982).

  20. The Goldie rank of prime supersolvable group algebras. Mitteilungen aus dem Math. Seminar Giessen 149, 115-129 (1981).

  21. On the Gelfand-Kirillov dimension of skew polynomial rings. J. Algebra 77, 186-188 (1982).

  22. Division algebras generated by finitely generated nilpotent groups. J. Algebra 85, 368-381 (1983).

  23. On the transcendence degree of group algebras of nilpotent groups. Glasgow Math. J. 25, 167-174 (1984).

  24. Group rings and division rings. In: F. van Oystaeyen (ed.), Methods in Ring Theory, pp. 265-280, D. Reidel Publ. Co., Dordrecht, 1984.

  25. On the cohomology of polycyclic-by-finite groups. J. Pure and Appl. Algebra 40, 87-98 (1986).

  26. (with M. Laska) Rational points on elliptic curves over Q in elementary abelian 2-extensions of Q. J. reine u. angew. Math. 355, 163-172 (1985).

  27. On Loewy lengths of projective modules for p-solvable groups. Comm. in Algebra 13, 1193-1212 (1985).

  28. K0 of skew group rings and simple Noetherian rings without idempotents. J. London Math. Soc. (2) 32, 41-50 (1985).

  29. On free subalgebras of certain division algebras. Proc. Amer. Math. Soc. 98, 401-405 (1986).

  30. On affine algebras. In: F. van Oystaeyen (ed.), Ring Theory, Lect. Notes in Mathematics No. 1197, pp. 121-126. Springer, Berlin-Heidelberg-New York, 1986.

  31. (with K.A. Brown and J. Howie) Induced resolutions and Grothendieck groups of polycyclic-by-finite groups. J. Pure and Appl. Algebra 53, 1-14 (1988).

  32. On the numerical local Langlands conjecture (after Koch and Zink). Contemporary Mathematics 86, 57-63 (1989).

  33. Frobenius reciprocity and G0 of skew group rings. In: J.L. Bueso, P. Jara, B. Torrecillas (eds.), Ring Theory, Lect. Notes in Mathematics No. 1328, pp. 165-172, Springer, Berlin-Heidelberg-New York, 1988.

  34. On Gelfand-Kirillov dimension and related topics. J. Algebra 118, 423-437 (1988).

  35. (with D. S. Passman) The structure of G0 for certain polycyclic group algebras and related algebras. Contemporary Mathematics 93, 283-302 (1989).

  36. Goldie ranks of prime polycyclic crossed products. In: F. van Oystaeyen and L. LeBruyn (eds.), Perspectives in Ring Theory, pp. 215-219, Kluwer Academic Publ., Dordrecht, 1988.

  37. The rank of G0 for polycyclic group algebras. In: S. Balcerzyk et al. (eds.), Topics in Algebra (Part 1), Banach Center Publications, Vol. 26, pp. 45-53, PWN, Warsaw, 1990.

  38. On the global dimension of fixed rings. Proc. Amer. Math. Soc. 106, 923-932 (1989).

  39. Crossed products: characters, cyclic homology, and Grothendieck groups. In: M. S. Montgomery and L. W. Small (eds.), Noncommutative Rings, MSRI Publications, Vol. 24, pp. 69-98, Springer, New York, 1992.

  40. (with K.A. Brown) Colimits of functors, and Grothendieck groups of infinite group algebras. In: L. Fuchs et al. (eds.), Abelian groups and noncommutative rings: A collection of papers in memory of Robert B. Warfield, Jr., Contemporary Mathematics 130, 89-109 (1992).

  41. On the homology of graded algebras. Comm. in Algebra 20, 489-507 (1992).

  42. (with K.A. Brown) Grothendieck groups of invariant rings and of group rings. J. Algebra 166, 423-454 (1994).

  43. (with K.A. Brown) Grothendieck groups and higher class groups of commutative invariants. In: L. A. Bokut et al. (eds.), Proceedings of the Second International Conference on Algebra. Dedicated to the memory of A. I. Shirshov. Contemporary Mathematics 184, 59-74 (1995).

  44. (with K.A. Brown) Grothendieck groups of invariant rings: filtrations. Proc. London Math. Soc. 67, 516-546 (1993).

  45. (with K.A. Brown) Grothendieck groups of invariant rings: examples. Comm. in Algebra 22, 279-306 (1994).

  46. (with M. E. Lorenz) On crossed products of Hopf algebras. Proc. Amer. Math. Soc. 123, 33-38 (1995).

  47. (with K.A. Brown) Grothendieck groups of invariant rings: linear actions of finite groups. Math. Zeitschr. 221, 113-137 (1996).

  48. (with M. E. Lorenz) Observations on crossed products and invariants of Hopf algebras. Archiv der Mathematik 63, 119-127 (1994).

  49. On Galois descent for Hochschild and cyclic homology. Comment. Math. Helv. 69, 474-482 (1994).

  50. Class groups of multiplicative invariants. J. Algebra 177, 242-254 (1995).

  51. Representations of finite dimensional Hopf algebras. J. Algebra 188, 476-505 (1997).

  52. Regularity of multiplicative invariants. Comm. in Algebra 24, 1051-1055 (1996).

  53. Picard groups of multiplicative invariants. Comment. Math. Helv. 72, 389-399 (1997).

  54. On the class equation for Hopf algebras. Proc. Amer. Math. Soc. 126, 2841-2844 (1998).

  55. K0 of invariant rings and nonabelian H1. J. Algebra 214, 458-478 (1999).

  56. (with Ed Letzter) Polycyclic-by-finite group algebras are catenary. Math. Res. Lett. 6, 183-194 (1999).

  57. Multiplicative invariants and semigroup algebras. Algebras and Representation Theory 4, 293-304 (2001).

  58. (with Nicole Lemire) On certain lattices associated with generic division algebras. J. Group Theory 3, 385-405 (2000).

  59. (with J. Pathak) On Cohen-Macaulay rings of invariants. J. Algebra 245, 247-264 (2001).

  60. (with Z. Reichstein, L.H. Rowen, and D.J. Saltman) Fields of definition of division algebras. J. London Math. Soc. 68, 651-670 (2003).

  61. On Euler classes of abelian-by-finite groups. J. Group Theory 6, 195-207 (2003).

  62. On the Cohen-Macaulay property of multiplicative invariants. Trans. Amer. Math. Soc. 358, 1605-1617 (2006).

  63. (with R. Guralnick) Orders of finite groups of matrices. In: ``Groups, Rings and Algebras: Proceedings of a Conference in Honor of Donald S. Passman'', Contemporary Mathematics 420, 141-162 (2006).

  64. (with Phùng Hô Hai) Koszul algebras and the quantum MacMahon Master Theorem. Bull. London Math. Soc. 39, 667-676 (2007).

  65. (with Phùng Hô Hai and Benoit Kriegk) N-homogeneous superalgebras. Journal of Noncommutative Geometry 2, 1-51 (2008).
  66. Group actions and rational ideals. Algebra and Number Theory 2, 467-499 (2008).
  67. Algebraic group actions on noncommutative spectra. Transformation Groups 14, 649-675 (2009).
  68. Some applications of Frobenius algebras to Hopf algebras. In: Groups, Algebras and Applications, Contemporary Mathematics, vol. 537, Amer. Math. Soc., Providence, RI, 2011, pp. 269-289.
  69. (with Loretta Tokoly) Projective modules over Frobenius algebras and Hopf comodule algebras. Comm. in Algebra 39, 4733-4750 (2011).
  70. Rational group actions on affine PI-algebras. Glasgow Math. J. 55A, 101-110 (2013).
  71. On the stratification of noncommutative prime spectra. Proc. Amer. Math. Soc. 142, 3013-3017 (2014).
  72. (with Adam Jacoby) Frobenius divisibility for Hopf algebras. Contemporary Math. 688, 125-137 (2017).
  73. (with Stefan Kolb, Bach Nguyen, and Ramy Yammine) On the adjoint representation of a Hopf algebra. Proc. Edinburgh Math. Soc. 63, 1092-1099 (2020).
  74. (with Bach Nguyen and Ramy Yammine) Actions of cocommutative Hopf algebras. J. Algebra 546, 703-722 (2020).
  75. Hopf algebra actions and rational ideals. Algebras and Representation Theory 25, 269-280 (2022).
  76. A note on affine representable algebras. (preprint, April 2021).