Research and Publications

Research Interests:

Richard Ng's present research interests lie in the area of Hopf algebra, quasi-Hopf algebra and tensor category. The main focus at the moment is aimed at the classification of finite dimensional Hopf algebras in special dimensions, and the study of invariants of pivotal tensor categories such as Frobenius-Schur indicators and exponents. This endeavor involves close ties with many other areas of mathematics such as representations of finite dimensional algebras and groups, knot invariants, etc. and the broadly conceived area of physical mathematics called conformal field theory.

Selected Publications (since 1997): MathSciNet and ArXiv.org

  1. Hopf algebras of dimension 2p2 (with Michael Hilgemann), Preprint, 16pp.

  2. Congruence Subgroups and Generalized Frobenius-Schur Indicators (with Peter Schauenburg), Preprint, 38pp.

  3. Hopf algebras of dimension pq, II , Journal of Algebra, 319 (2008), no. 7, 2772--2788 (doi:10.1016/j.jalgebra.2007.08.003).

  4. On Radicals of Module Coalgebras (with Yuqun Chen and Kar-Ping Shum), Journal of Pure and Applied Algebra, 212 (2008), no. 1, 157--167 (doi:10.1016/j.jpaa.2007.05.009).

  5. On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups (with Christopher Goff and Geoffrey Mason), Journal of Algebra, 312 (2007), no. 2, 849--875.

  6. Frobenius-Schur Indicators and Exponents of Spherical Categories (with Peter Schauenburg), Advances in Mathematics, 211 (2007), no. 1, 34--71 (doi:10.1016/j.aim.2006.07.017).

  7. Central Invariants and Higher Indicators for Semisimple Quasi-Hopf Algebras (with Peter Schauenburg) Transactions of the American Mathematical Society, 360 (2008), 1839-1860 (doi:10.1090/S0002-9947-07-04276-6).

  8. Higher Frobenius-Schur Indicators for Pivotal Categories (with Peter Schauenburg)  Contemporary Mathematics  441, 63-90 (ISBN-10: 0-8218-4195-5).

  9. Reciprocity for Multirestricted Stirling Numbers (with Ji Young Choi, Ling Long, Jonathan Smith) Journal of Combinatorial Theory, Series A, 113 (2006), no. 6, 1050--1060.

  10. Hopf Algebras of Dimension 2p, Proceedings of the American Mathematical Society, 133 (2005), 2237--2242.

  11. Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras, (with Geoffrey Mason) Advances in Mathematics, 190 (2005), 161--195.

  12. Hopf Algebras of Dimension pq, Journal of Algebra, 276 (2004), 399--406.

  13. Hopf Algebras of Dimension p2, Hopf algebras, 193--201, Lecture Notes in Pure and Appl. Math., 237, Dekker, New York, 2004. 

  14. Non-Semisimple Hopf Algebras of Dimension p2, Journal of Algebra, 255 (2002), 182--197.

  15. Non-commutative, Non-cocommutative Semisimple Hopf Algebras arise from Finite Abelian Groups, Groups, Rings, Lie and Hopf Algebras (St. John's, NF, 2001), 167--177, Math. Appl., 555, Kluwer Acad. Publ., Dordrecht, 2003 (ISBN: 1402012209).

  16. Group cohomology and gauge equivalence of some twisted quantum doubles, (with Geoffrey Mason) Transactions of the American Mathematical Society, 353 (2001), 3465-3509.

  17. Classification of the Lie bialgebra structures on the Witt and Virasoro algebras, (with Earl Taft)  Journal of Pure and Applied Algebra, 151 (2000), 67--88.

  18. On the projectivity of module coalgebras, Proceedings of the American Mathematical Society, 126 (1998), 3191--3198.

  19. Quantum convolution of linearly recursive sequences, (with Earl Taft) Journal of Algebra, 198 (1997), 101--119.