M. Susan Montgomery
 Professor

MAILING ADDRESS: 3620 Vermont Ave, KAP 108
Los Angeles, California 90089-2532
PHONE: (213) 740-2419
FAX: (213) 740-2424
OFFICE: DRB 240
EMAIL: smontgom@usc.edu

Personal

Native of Lansing, Michigan
Married, three stepsons; three nieces, one nephew, five great-nieces and nephews


Research Interests

My current research interests concern non-commutative algebras:
in particular, Hopf algebras, their structure and representations,
and their actions on other algebras.


Education

University of Michigan, B.A. (with highest honors) 1965
University of Chicago, S.M. 1966, Ph.D. 1969


Employment

DePaul University, Chicago: Assistant Professor 1969-70
University of Southern California:

Assistant Professor 1970-75
Associate Professor 1975-82
Professor 1982-present


Editing

AMS Math Surveys and Monographs, 1983-90 (Chair 89-90)
Journal of Algebra, 1987-2007
AMS Proceedings, Coordinating Editor for Algebra and Number Theory, 1992-96
Advances in Math, 1995-2002
Journal of Algebras and Representation Theory, 1998 - present
Algebra and Number Theory, 2008 - present


Other Professional Activities/Recognition

NSF Research Grant, 1971-2009 (sole PI since 1978)
John S. Guggenheim Memorial Foundation Fellow, 1984-85
AMS Invited Hour Address, AMS Annual Meeting, Louiville, 1984
Raubenheimer Distinguished Faculty Award, Division of Natural Sciences and Mathematics,
University of Southern California, 1986
AMS Board of Trustees, 1986-96 (Chair, 1989 and 1994)
CBMS Lecturer, DePaul University, Chicago, 1992
Board on Math Sciences (BMS) of the National Research Council, 1995-98
Invited Hour Address, AMS-Israel Math Union Joint Meeting, Jerusalem, 1995
AMS-SMM Lecturer, Annual Meeting of the Sociedad Matematica Mexicana, Aguascalientes, 1997
Co-organizer, MSRI Year on Non-commutative Algebra, 1999-2000
AMS Invited Hour Address, AMS Sectional Meeting, Bowling Green, Kentucky, 2005


Publications

Books

  1. Selected Papers on Algebra (co-chair of editorial committee), Raymond W. Brink Selected Mathematical Papers, vol 3, Mathematical Association of America, Washington DC, 1977.
  2. Fixed Rings of Finite Automorphism Groups of Associative Rings , Lecture Notes in Math 818, Springer-Verlag, New York, 1980.
  3. Group Actions on Rings (editor), Proceedings of Joint Summer Research Conference, AMS Contemporary Math, vol 43, AMS 1985.
  4. Non-Commutative Rings (co-editor with L. W. Small), MSRI Publications, vol 24, Springer-Verlag, 1992.
  5. Advances in Hopf Algebras (co-editor with Jeffrey Bergen), Lecture Notes in Pure and Applied Math 158, Marcel Dekker, 1994.
  6. Hopf Algebras and Their Actions on Rings, CBMS Lecture Notes vol 82, American Math Society, Providence, RI, 1993 (238 pages).
  7. New Directions in Hopf Algebras (co-editor with H.-J. Schneider), MSRI Publications, vol. 43, Cambridge University Press, 2002.

Papers (since 1995)

  1. Indecomposable coalgebras, simple comodules, and pointed Hopf Algebras, AMS Proceedings 123 (1995), 2343-2351.
  2. Hopf crossed products, rings of quotients, and prime ideals (with H.-J. Schneider), Advances in Math 112 (1995), 1-55.
  3. On the generalized Lie structure of associative algebras (with Yu. Bahturin and D. Fischman), Israel J. Math 96 (1996), 27-48.
  4. Basic coalgebras (with W. Chin), in Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras, V. Chari and I. Penkov, editors, AMS/International Press vol 4 (1997), 41-47.
  5. Frobenius extensions of subalgebras of Hopf Algebras (with D. Fischman and H.-J. Schneider), AMS Transactions 349 (1997), 4857-4895.
  6. Constructing simple Lie superalgebras from associated graded algebras, J. of Algebra 195 (1997), 558-579.
  7. Nil subsets of graded algebras (with L. W. Small), AMS Proceedings 126 (1998), 653-656.
  8. Irreducible representations of crossed products (with S. Witherspoon), J. Pure Applied Algebra, 129 (1998), 315-326.
  9. PI-envelopes of Lie superalgebras (with Yu. Bahturin), AMS Proceedings 127 (1999), 2829-2839.
  10. Prime ideals in Hopf Galois extensions (with H.-J. Schneider), Israel J. Math, 112 (1999), 187-235.
  11. On Yetter-Drinfeld categories and H-commutativity (with M. Cohen and D. Fischman), Communications in Algebra 27 (1999), 1321-1345.
  12. Classifying Finite-Dimensional Semisimple Hopf Algebras, AMS Contemporary Math 229 (1998), 265-279.
  13. A Frobenius-Schur theorem for Hopf algebras (with V. Linchenko), J. of Algebras and Representation Theory 3 (2000), 347-355.
  14. Bicharacters, twistings, and Scheunert's theorem for Hopf algebras (with Yu. Bahturin and D. Fischman), J. of Algebra 236 (2001), 246-276.
  15. Skew-derivations of finite-dimensional algebras and actions of the double of the Taft Hopf algebra (with H.-J. Schneider), Tsukuba J. of Math 25 (2001), 337-358.
  16. Representation theory of finite-dimensional semisimple Hopf algebras, Algebra - Representation Theory (Constanta, 2000), K. W. Roggenkamp and M. Stefanescu, editors, NATO Sci. Ser. II Math. Phys. Chem. 28, Kluwer, Dordrecht, 2001, 189-218.
  17. Polycharacters of cocommutative Hopf algebras (with Yu. Bahturin and M. Kochetov), Canadian Math Bulletin 45 (2002), 11-24.
  18. Computing the Frobenius-Schur indicator for abelian extensions of Hopf algebras (with Y. Kashina and G. Mason), J. of Algebra 251 (2002), 888-913.
  19. Generalized Lie solvability of associative algebras (with Yu. Bahturin and M. Zaicev), Groups, Rings, Lie, and Hopf Algebras , Yu. Bahturin, editor, Proceedings of the 2001 St. John's conference, Kluwer, 2003, 1-23.
  20. Algebra properties invariant under twisting, Hopf algebras in Non-commutative Geometry and Physics, S. Caenepeel and F. Van Oystaeyen, editors, Lecture Notes in Pure and Applied Math, vol 239, Marcel Dekker, 2005, 61-75.
  21. Krull relations in Hopf Galois extensions: lifting and twisting (with H._J. Schneider), Journal of Algebra 288 (2005), 364-383.
  22. Stable Jacobson radicals and semiprime smash products (with V. Linchenko and L. W. Small), Bulletin London Math Society 37 (2005), 860-872.
  23. Primitive ideals and Jacobson radicals in Hopf Galois extensions, Proceedings of the XV Coloquio Latinoamericano de Algebra, AMS Contemporary Math 376, 2005, 333-344.
  24. Hopf powers and orders for some bismash products (with R. Landers and P. Schauenburg), Journal of Pure and Applied Algebra 205 (2006), 156-188.
  25. Semiprime smash products and H-stable prime radicals for PI- algebras (with V. Linchenko), AMS Proceedings 135 (2007), 3091-3108.
  26. Frobenius-Schur indicators for subgroups and the Drinfel'd double of Weyl groups (with R. M. Guralnick), AMS Transactions, to appear.
  27. Representations of some Hopf algebras associated to the symmetric group S_n (with A. Jedwab), Algebras and Representation Theory 12 (2009), 1-17.
  28. Group gradings on simple Lie algebras in finite characteristic (with Yu. Bahturin and M. Kochetov), AMS Proceedings 137 (2009), 1245-1254.