(1) Lie Algebras and Their Representation Theory;
(2) Quantizations of Lie Bialgebras;
(3) Quantum Groups and Their Representation Theory;
(4) Deformation Quantization and Related Topics.
Papers published:
[1] Notes on two-parameter quantum groups‚ (II)‚ (with Y.F. Pei)‚ Comm. Algebra 40 (9) (2012)‚ 3202--3220. arXiv:0908.1635v1.
[2] Leibniz algebras graded by finite root systems of type C_l‚ (with D. Liu)‚ Siberian Math. J.‚ 53 (3) (2012)‚ 490--501.
[3] Leibniz superalgebras graded by finite root systems‚ (with D. Liu‚ L. Zhu)‚ Proceedings of the International Conference on Operads and Universal Algebra‚ Nankai Series in Pure‚ Applied Math. and Theoret. Phys. vol. 9 (2012)‚ Edited by C. Bai‚ L. Guo‚ J-L. Loday‚ Tianjin‚ China‚ 2010‚ pp. 51--68.
[4] Cyclic homology of the strong smash product algebras‚ (with J. Zhang)‚ Journal für die Reine und Angewandte Mathematik. [Crelle´s Journal]‚ Heft. 663 (2012)‚ 177---207.
[5] Heisenberg Lie color algebras. (with H. Yang)‚ Comm. Algebra‚ 39 (5) (2011)‚ 1782-1795.
[6] Twists and Quantizations of Cartan type S Lie algebras‚ (with X.L. Wang)‚ J. Pure and Applied Algebra‚ 215 (6) (2011)‚ 1205---1222.
[7] Introduction to co-split Lie bialgebras‚ (with L.M. Xia)‚ Algebra Represent. Theory‚ 14 (1)‚ (2010)‚ 191---199.
[8] Leibniz algebras graded by finite root systems‚ (with D. Liu)‚ Algebra Colloq. 17 : 3 (2010)‚ 431---446.
[9] Convex PBW-type Lyndon bases and restricted two-parameter quantum groups of type B‚ (with X.L. Wang)‚ arXiv:0812.3343‚ J. Geom. Phys. 60 (2010)‚ 430---453.
[10] Multiparameter quantum groups and quantum shuffles‚ (I)‚ (with Y.F. Pei‚ M. Rosso)‚ in Quantum Affine Algebras‚ Extended Affine Lie Algebras‚ and Their Applications‚ Contemporary Mathematics‚ vol. 506‚ Amer. Math. Soc.‚ Providence‚ RI‚ 2010‚ pp. 145-171. arXiv:0811.0129.
[11] Cosplit Lie superalgebra of type A(m‚n)‚ (in Chinese) (with L.M. Xia)‚ Chin. Ann. Math. 30 A (1) (2009)‚ 127--130.
[12] Convex PBW-type Lyndon basis and restricted two-parameter quantum groups of type G_2‚ (with X.L. Wang)‚ Pacific J. Math. 241 (2) (2009)‚ 243–273‚ arXiv.0811.0209.
[13] Two-parameter quantum affine algebra U_{r‚s}(\widetilde {sl}_n)‚ Drinfeld realization and quantum affine Lyndon basis‚ (with M. Rosso‚ H.L. Zhang)‚ Comm. Math. Phys.‚ 278 (2) (2008)‚ 453—486‚ arXiv:0812.3107.
[14] A cohomological characterization of Leibniz central extensions of Lie algebras‚ (with Y.F. Pei‚ D. Liu)‚ Proc. Amer. Math. Soc.‚ 136 (2) (2008)‚ 437—447‚ arXiv.math.QA/0605399.
[15] Notes on two-parameter quantum groups‚ (I)‚ (with Y.F. Pei)‚ Sci. in China‚ Ser. A. 51 (6) (2008)‚ 1101--1110‚ arXiv.math.QA/0702298.
[16] Two-parameter quantum groups of exceptional type E-series and convex PBW type basis‚ (with X.T. Bai)‚ Algebra Colloq. 15:4 (2008)‚ 619---636‚ arXiv.math.QA/0605179.
[17] Quantizations of generalized-Witt algebra and of Jacobson-Witt algebra in the modular case‚ (with X.L. Wang)‚ Journal of Algebra 312‚ (2007)‚ 902--929‚ arXiv.math.QA/0602281.
[18] The two-parameter quantum group of exceptional type G_2 and Lusztig´s symmetries‚ (with Q. Shi)‚ Pacific J. Math. Vol. 230 (2)‚ (2007) 327--346‚ arXiv.math.QA/0601444.
[19] Representations of two-parameter quantum orthogonal and symplectic quantum groups‚ (with N. Bergeron‚ Y. Gao)‚ AMS/IP Studies in Advanced Mathematics‚ vol. 39 (2007)‚ 1--21‚ arXiv.math.QA/0510124.
[20] Universal central extensions of the matrix Leibniz superalgebras sl(m‚ n‚ A)‚ (with D. Liu)‚ Comm. Algebra 35‚ (2007)‚ 1814--1823‚ arXiv.math.RT/0610579.
[21] Drinfeld doubles and Lusztig´s symmetries of two-parameter quantum groups‚ (with N. Bergeron‚ Y. Gao)‚ Journal of Algebra 301 (2006)‚ 378--405‚ arXiv.math.RT/0505614.
[22] Leibniz superalgebras and central extensions‚ (with D. Liu)‚ J. Algebra and Its Applications 5 (6) (2006)‚ 765--780‚ arXiv.math.RT/0510546.
[23] Vertex representations for toroidal Lie algebra of type G_2‚ (with D. Liu)‚ J. Pure Applied Algebra 198 (2005)‚ 257--279.
[24] Steinberg unitary Leibniz algebras‚ (with D. Liu)‚ Linear Algebra and its Application‚ 405 (2005)‚ 279--303.
[25] Decompositions of bosonic modules of Lie algebras W_{1+\infty} and W_{1+\infty}(gl_n)‚ (with D. Liu)‚ Chin. Ann. of Math.B:4 (2005)‚ 633--642.
[26] Quasi L_n filiform Lie algebras‚ (with B. Ren)‚ Comm. Algebra 33 (2)‚ (2005)‚ 633--648.
[27] Irreducible representations for Virasoro-toroidal Lie algebras‚ (with L.M. Xia)‚ J. Pure Applied Algebra 194 (2004)‚ 213--237.
[28] The derivation algebras and 2-cocycles of the algebras of q-differential operators‚ (with D. Liu)‚ Comm. Algebra 32(11)‚ (2004)‚ 4387--4413.
[29] Leibniz central extensions on some infinite-dimensional algebras‚ (with D. Liu)‚ Comm. Algebra 32 (6)‚ (2004)‚ 2385--2405.
[30] Quantum group structure associated to the quantum affine space‚ Algebra Colloq. 11(4)‚ (2004)‚ 483--492.
[31] Realization of quantized algebra of type A as Hopf algebra over quantum space‚ Comm. Algebra 29 (2)‚ (2001) 529---539.
[32] Quantum divided power algebra‚ q-derivatives‚ and some new quantum groups‚ Journal of Algebra 232 (2)‚ (2000)‚ 507---540‚ arXiv:0902.2858.
[33] q-Witt algebra‚ q-Lie algebra‚ q-holomorph structure and representations‚ Algebra Colloq.6 (1)‚ (1999) 51---70‚ arXiv.math/0512526.
[34] Quantum group structure of q-deformed Virasoro algebra‚ Lett. Math. Phys. 44 (2)‚ (1998) 99---103.
[35] On representations of the Witt algebra‚ (with G.Y. Shen)‚ Chin. Sci. Bull. 43 (1)‚ (1998) 189---192.
[36] Graded modules for the Poisson algebras‚ Chin. Ann. Math.17B:4‚ (1996) 515---522.
[37] Irreducible constitutes of graded modules for graded contact Lie algebras of Cartan type‚ Comm. Algebra 22 (14)‚ (1994) 5951---5971.
[38] The graded modules for graded contact Cartan algebras‚ Comm. Algebra 22 (11)‚ (1994) 4475---4497.
[39] A class of generalized eta functions and string functions of affine Lie algebras‚ Chin. Ann. Math.15A:4‚ (1994) 426—432.
[40]《度量向量空间与典型群引论》（华东师大高年级选修课讲义‚ 与陈志杰合作编译‚1999）。
Preprints:
[1] Vertex representations of two-parameter quantum affine algebras U_{r‚s}(\widehat{\frak{g}}): the simply-laced cases‚ (with H.L. Zhang)‚ Preprint 2006—2007.
[2] Vertex representations of two-parameter quantum affine algebras U_{r‚s}(\widehat{\frak{g}}): the nonsimply-laced cases‚ (with H.L. Zhang)‚ Preprint 2006—2007.
[3] Lyndon words‚ convex PBW bases and their R-matrices for the two-parameter quantum groups of B_2‚C_2‚D_4 types‚ (manuscript) 2005.
[4] Realization of U_q(sp_2n) within the q-differential algebra on quantum symplectic space‚ (with J. Zhang)‚ Preprint 2007.
[5] Notes on two-parameter quantum groups‚ (II)‚ (with Y.F. Pei)‚ Preprint 2008‚ arXiv:0908.1635v1.
[6] Vertex representations for toroidal Lie algebra of type C‚ (with L.M. Xia)‚ Preprint 2005.
[7] Vertex representations for twisted affine Lie algebra of type A_2l^(2)‚ (with L.M. Xia)‚ (submitted)‚ Preprint 2005.
[8] The theory of the Cartan type q-Lie algebras and noncommutative geometry on the Manin’s quantum affine space‚ I (with C. Kassel and H. Strade)‚ Preprint 2001.
