My research lies in the area of deformations, quantizations and representations of algebraic structures. Keywords include deformation theory of algebras, deformation quantization, quantum groups, Hochschild cohomology, universal deformation formulas, Frobenius Lie algebras, Drinfel'd twists, Yang-Baxter equations, generalized quantum Schur algebras.
- Cellular bases of generalised q-Schur algebras, Mathematical Proceedings of the Cambridge Philosophical Society, (2016), in press.
- Deformations associated with rigid algebras, Journal of Homotopy and Related Structures 10 (2015), no. 3, 437-458.
- On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra, Journal of Pure and Applied algebra 218 (2014), no. 5 , 879--887. (with M. Gerstenhaber)
- Meander graphs and Frobenius seaweed algebras, Journal of Generalized Lie Theory, Volume 5 (2011), Article ID G110103, 7 pages. (With V. Coll and C. Magnant)
- Topics in algebraic deformation theory. Higher Structures in Geometry and Physics, 1-24, Progress in Mathematics 287, Springer, New York, 2010.
- The principal element of a Frobenius Lie algebra. Lett. Math. Phys. 88 (2009), no. 1-3, 333–341.
- On the defining relations for generalized q-Schur algebras.
Adv. Math. 221 (2009), no. 3, 955–982. (With S. Doty and J. Sullivan)
- Presenting generalized Schur algebras in types B, C, and D.
Adv. Math. 206 (2006), no. 2, 434–454. (With S. Doty and J. Sullivan)
- Diagrams of Lie algebras.
J. Pure Appl. Algebra 196 (2005), no. 2-3, 169–184. (With M. Gerstenhaber and S.D. Schack)
- Quantum groups and deformation quantization: explicit approaches and
J. Math. Phys. 45 (2004), no. 10, 3703–3741. (With P Bonneau, M. Gerstenhaber and D. Sternheimer)
- Presenting Schur algebras as quotients of the universal enveloping
algebra of gl(2).
Algebr. Represent. Theory 7 (2004), no. 1, 1–17. (With S. Doty)
- Algebraic deformations arising from orbifolds with discrete
J. Pure Appl. Algebra 187 (2004), no. 1-3, 51–70. (With A.
Căldăraru and S. Witherspoon)
- Presenting Schur algebras.
Int. Math. Res. Not. 2002, no. 36, 1907–1944. (With S. Doty)
- The Donald-Flanigan problem for finite reflection groups.
EuroConférence Moshé Flato 2000, Part I (Dijon).
Lett. Math. Phys. 56 (2001), no. 1, 41–72. (With M. Gerstenhaber and M. Schaps)
- Generators and relations for Schur algebras.
Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 54–62 (electronic). (With S. Doty)
- Compatible deformations.
Trends in the representation theory of finite-dimensional algebras
(Seattle, WA, 1997),
159–168, Contemp. Math., 229, Amer. Math. Soc., Providence, RI, 1998. (With M. Gerstenhaber)
- Boundary solutions of the quantum Yang-Baxter equation and solutions in
Lett. Math. Phys. 44 (1998), no. 2, 131–141. (With M. Gerstenhaber)
- Bialgebra actions, twists, and universal deformation formulas.
J. Pure Appl. Algebra 128 (1998), no. 2, 133–151. (With J.J. Zhang)
- Nonstandard solutions of the Yang-Baxter equation.
Lett. Math. Phys. 44 (1998), no. 1, 67–75. (With T. J. Hodges)
- Boundary solutions of the classical Yang-Baxter equation.
Lett. Math. Phys. 40 (1997), no. 4, 337–353. (With M. Gerstenhaber)
- Quantum Weyl algebras.
J. Algebra 176 (1995), no. 3, 861–881. (With J.J. Zhang)
- Construction of quantum groups from Belavin-Drinfelʹd
Quantum deformations of algebras and their representations (Ramat-Gan,
1991/1992; Rehovot, 1991/1992),
45–64, Israel Math. Conf. Proc., 7, Bar-Ilan Univ., Ramat Gan, 1993. (With M. Gerstenhaber and S.D. Schack)
- Quantum groups, cohomology, and preferred deformations.
Proceedings of the XXth International Conference on Differential
Geometric Methods in Theoretical Physics, Vol. 1, 2 (New York, 1991),
529–538, World Sci. Publ., River Edge, NJ, 1992. (With M. Gerstenhaber and S.D. Schack)
- Quantum symmetry.
Quantum groups (Leningrad, 1990),
9–46, Lecture Notes in Math., 1510, Springer, Berlin, 1992. (With M. Gerstenhaber and S.D. Schack)
- Quantization of tensor representations and deformation of matrix
J. Pure Appl. Algebra 79 (1992), no. 2, 169–190.
- Separable functors revisited.
Comm. Algebra 18 (1990), no. 5, 1445–1459. (With F. Van Oystaeyen)
- An explicit deformation formula with noncommuting derivations, Ring theory (Ramat Gan and Jerusalem, 1988/1989),
396–403, Israel Math. Conf. Proc., 1, Weizmann, Jerusalem, 1989. (With V. Coll and M. Gerstenhaber)