Tim Hodges

Publications

Journal Articles

• Dimension of the linearization equations of the Matumoto-Imai cryptosystems, to appear in the Proceedings of the International Workshop on Coding and Cryptography, Bergen (Norway), 2005.
• Triangular poisson structures on Lie groups and symplectic reduction, in "Noncommutative Geometry and Representation Theory in Mathematical Physics", Contemp. Math. 391 (2005), 123-134 (with M. Yakimov).
• Degenerations and representations of twisted Shibukawa-Ueno R-operators, Lett. Math. Phys., 68 (2004), 151-164 (with R. Endelman).
• Cryptanalysis of an implementation scheme of the tamed transformation method cryptosystem, J. Alg. Appl., 3 (2004), 273-282. (with J. Ding).
• The Yang-baxter equation for operators on function fields, Quantum groups and Lie theory (Durham, 1999), 168--174, London Math. Soc. Lecture Note Ser., 290, Cambridge Univ. Press, Cambridge, 2001. (with J. Ding)
• The double and dual of a quasi-triangular Lie algebra, Math. Res. Let., 8 (2001), 91-105 (with M. Yakimov).
• Generating functions for the coefficients of the Cremmer-Gervais R-matrices, J. Pure Appl. Algebra, 157 (2001), 69-79.
• Generalized Jordanian matrices of Cremmer-Gervais type, Lett. Math. Phys., 52 (2000), 225-237 (with R. Endelman).
• The Cremmer-Gervais solution of the Yang-Baxter equation, Proc. Amer. Math. Soc. 127 (1999), 1819-1826.
• Non-standard solutions of the Yang-Baxter equation, Lett. Math. Phys., 44 (1998), 67 - 75 (with A. Giaquinto).
• Non-standard quantum groups associated to Belavin-Drinfeld triples, Contemp. Math., 214 (1998), 63-70.
• Double quantum groups and Iwasawa decomposition, J. Algebra, 192 (1997), 303-325.
• Algebraic structure of multi-parameter quantum groups, Advances in Math. 126 (1997), 52 - 92, (with T. Levasseur and M. Toro).
• On the Cremmer-Gervais quantizations of SL(n), International Mathematics Research Notices, 10 (1995), 465-481.
• Primitive ideals of C_q[SL(n)], J. Algebra 168 (1994), 455-468 (with T. Levasseur).
• Primitive ideals of the quantum group C_q[SL(3)], Comm. Math. Phys. 156 (1993), 581-605 (with T. Levasseur).
• Chern characters, reduced ranks and D-modules on the flag variety, Proc. Edin. Math. Soc. (1994) 37, 477-482 (with M. P. Holland).
• Noncommutative deformations of type A Kleinian singularities, J. Algebra 161 (1993), 271-290.
• Morita equivalence of primitive factors of U( sl(2,C)), in ``Kazhdan-Lusztig Theory and Related Topics,'' V. Deodhor, ed. Contemporary Mathematics, Vol. 139 (1992), 175-180.
• On the Krull dimension of tensor products of algebras, Comm. Algebra, 19(1991), 143-156 (with K. Lee and R. Resco).
• Ring theoretical aspects of the Bernstein-Beilinson theorem, in ``Proceedings of the Midwest Ring Theory Conference in Athens, Ohio''. Lecture Notes in Mathematics 1448, Springer-Verlag 1990, 155-164.
• Fixed rings of Weyl algebras, J. Algebra, 130(1990) 83-96 (with J. Alev and J. Velez).
• K-theory of D-modules and primitive factors of the enveloping algebra of a semisimple Lie algebra, Bull. Sci. Math., 113(1989), 85-88.
• Noetherian rings with big indecomposable projective modules, Bull. London Math. Soc., 21(1989) 249-254 (with J.T. Stafford).
• K-theory of Noetherian rings, Seminaire d'Algebre Mme Malliavin, LNM 1404, 246-269, Springer (1989).
• Representing Clifford algebras as cross-products, J. Algebra, 123(1989) 500-505 (with S. Tesser).
• Equivariant K-theory of Noetherian rings, J. London Math. Soc., 39(1989), 414-426.
• A noncommutative Bass-Tate sequence, Bull. Soc. Math. Belg., (1987), 255-257.
• An indecomposable projective module over a Noetherian domain of Krull dimension one, Bull. London Math. Soc., 19(1987), 139-144 (with J. Osterburg).
• K-theory and right ideal class groups for HNP rings, Trans. Amer. Math. Soc., 302(1987), 751-767.
• On the primitivity of polynomial rings with non-primitive coefficient rings, Proc. Amer. Math. Soc., 98(1986), 553-558.
• The global dimension of certain primitive factors of the enveloping algebra of a semi-simple Lie algebra, J. London Math. Soc. (2), 82(1985), 411-418 (with S.P. Smith).
• Sheaves of noncommutative algebras and the Bernstein-Beilinson equivalence of categories, Proc. Amer. Math. Soc., 93(1985), 379-386 (with S.P. Smith).
• Krull and global dimensions of Weyl algebras over division rings, J. Algebra, 91(1984), 334-359 (with K.R. Goodearl and T.H. Lenagan).
• An example of a primitive polynomial ring, J. Algebra, 90(1984) 217-219.
• The Krull dimension of skew-Laurent extensions of commutative Noetherian rings, Comm. Alg., 12(1984), 1301-1310.
• On Ore and skew-Laurent extensions of Noetherian rings, J. Algebra, 73(1981), 56-64 (with J.C. McConnell).

The papers listed below have been occasionally cited in the literature. The link explains the availability or revised published form of the work.

• Differential operators on the flag variety and the Conze embedding, (with S.P. Smith).
• Primitive ideals of the quantum group Cq[G], (with T. Levasseur).

Book Reviews

• "Torsion Theories", by J.S. Golan, Bull. Amer. Math. Soc., 20(1989) 148-151.
• "A guide to quantum groups", by V. Chari and A. Presley, Bull. London Math. Soc., 29 (1997), 506-508.