教育及工作经历
2007- 苏州大学数学科学学院
2005-2007 中科院数学所博士后
2003-2005 北京大学数学学院博士后
2000-2003 中科院系统所博士
1993-2000 苏州大学数学学院本科、硕士研究生
研究方向
主要从事李代数的研究工作。先后主持国家自然科学基金项目3项，参与3项. 在Advances in Mathematics, Documenta Mathematica, Journal of Algebra, Communications in Contemporary Mathematics等SCI杂志上发表学术论文30余篇。
41 Hu, jinxin; Lü, Rencai; Classification of simple Harish-Chandra modules of the Cartan type Lie algebra \bar{S}_2， to appear in J. Algebra.
40 Y. Cai, R.Lü ,X. Wang, Non-weight modules over the Lie (super)algebras related to the Virasoro algebra, J. Algebra {\bf 683} (2025), 834--857; MR4936484
39 Yan-an Cai;Rencai Lü;Yaohui Xue;Classification of Simple Strong Harish-Chandra Modules Over the Lie Superalgebra of Vector Fields on $C^{m|n}$, to appear in Transformation Groups.
38 R. Lü, Y. Xue, Classification of simple Harish-Chandra modules over the generalized Witt algebras, J. Algebra {\bf 650} (2024), 54--79; MR4733241
37 Y. Cai, Y. He ,R. Lü, Module structures on U(S^-) for the Schr\"odinger algebra, J. Geom. Phys. {\bf 191} (2023), Paper No. 104919, 8 pp.; MR4618896
36 Lü, Rencai; Xue, Yaohui;Bounded weight modules over the Lie superalgebra of Cartan W-type, Algebr. Represent. Theory 26 (2023), no. 3, 763–781.
35 Xue, Yaohui; Lü, Rencai; Classification of simple bounded weight modules of the Lie algebra of vector fields on $\bC^n$, Israel J. Math. 253 (2023), no. 1, 445–468.
34 Cai, Yan-an, Lü, Rencai, Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact algebra, J. Pure Appl. Algebra 226 (2022), no. 3, Paper No. 106866, 14 pp.
33 Xue, Yaohui; Lü, Rencai;Simple weight modules with finite-dimensional weight spaces over Witt superalgebras, J. Algebra 574(2021), 92-116.
32 Cai, Yan-an; Lü, Rencai; Wang,Yan; Classification of simple Harish-Chandra modules for map (super)algebras related to the Virasoro algebra, Journal of Algebra, 570(2021),397-415
31 Cai, Yan-an; Liu, Dong; Lü, Rencai; Classification of simple Harish-Chandra modules over the N = 1 Ramond algebra, Journal of Algebra Volume 567(2021),114-127
30 Lü, Rencai; Zhao, Kaiming Generalized oscillator representations of the twisted Heisenberg-Virasoro algebra. Algebr. Represent. Theory 23 (2020), no. 4, 1417–1442.
29 Guo, Xiangqian; Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; Simple Witt modules that are finitely generated over the Cartan subalgebra. Mosc. Math. J. 20 (2020), no. 1, 43–65.
28 He, Yan; Cai, Yan-an; Lü, Rencai; A class of new simple modules for sln+1 and the Witt algebra. J. Algebra 541 (2020), 415–435.
27 Brešar, Matej; Guo, Xiangqian; Liu, Genqiang; Lü, Rencai; Zhao, Kaiming; Zero product determined Lie algebras. Eur. J. Math. 5 (2019), no. 2, 424–453.
26 Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; Irreducible Witt modules from Weyl modules and gln-modules. J. Algebra 511 (2018), 164–181.
25 Futorny, Vyacheslav; Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; New families of irreducible weight modules over sl3. J. Algebra 501 (2018), 458–472.
24 Cox, Ben; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Simple superelliptic Lie algebras. Commun. Contemp. Math. 19 (2017), no. 3, 1650032, 22 pp.
23 Lü, Rencai; Zhao, Kaiming; A family of simple weight modules over the Virasoro algebra. J. Algebra 479 (2017), 437–460.
22 Adamović, Dražen; Lü, Rencai; Zhao, Kaiming; Whittaker modules for the affine Lie algebra A(1)1. Adv. Math. 289 (2016), 438–479.
21 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Classification of simple weight modules over the 1-spatial ageing algebra. Algebr. Represent. Theory 18 (2015), no. 2, 381–395.
20 Lü, Rencai; Zhao, Kaiming; Finite-dimensional simple modules over generalized Heisenberg algebras. Linear Algebra Appl. 475 (2015), 276–291.
19 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Simple weight modules over weak generalized Weyl algebras. J. Pure Appl. Algebra 219 (2015), no. 8, 3427–3444.
18 Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; A class of simple weight Virasoro modules. J. Algebra 424 (2015), 506–521.
17 Dubsky, Brendan; Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Category O for the Schrödinger algebra. Linear Algebra Appl. 460 (2014), 17–50.
16 Lu, Rencai; Zhao, Kaiming; Irreducible Virasoro modules from irreducible Weyl modules. J. Algebra 414 (2014), 271–287.
15 Cox, Ben; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; n-point Virasoro algebras and their modules of densities. Commun. Contemp. Math. 16 (2014), no. 3, 1350047, 27 pp.
14 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; On simple modules over conformal Galilei algebras. J. Pure Appl. Algebra 218 (2014), no. 10, 1885–1899.
13 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Fraction representations and highest-weight-like representations of the Virasoro algebra. J. Algebra 387 (2013), 68–86.
12 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras. Proc. Edinb. Math. Soc. (2) 55 (2012), no. 3, 697–709.
11 Lü, Rencai; Guo, Xiangqian; Zhao, Kaiming; Irreducible modules over the Virasoro algebra. Doc. Math. 16 (2011), 709–721.
10 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra. Forum Math. 23 (2011), no. 5, 1029–1052.
9 Lü, Rencai; Zhao, Kaiming; Classification of irreducible weight modules over the twisted Heisenberg-Virasoro algebra. Commun. Contemp. Math. 12 (2010), no. 2, 183–205.
8 Lü, Rencai; Zhao, Kaiming; Verma modules over quantum torus Lie algebras. Canad. J. Math. 62 (2010), no. 2, 382–399.
7 Batra, Punita; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Highest weight modules over pre-exp-polynomial Lie algebras. J. Algebra 322 (2009), no. 12, 4163–4180.
6 Lü, RenCai; Weight modules over some Block algebras. Sci. China Ser. A 52 (2009), no. 3, 517–525.
5 Lü, Rencai; Classification of quasifinite modules with nonzero central charges for EALAs of Type A with coordinates in quantum torus. Chin. Ann. Math. Ser. B 30 (2009), no. 2, 129–138.
4 Lü, Rencai; Zhao, Kaiming; Structure of Weyl type Lie algebras. J. Algebra 306 (2006), no. 2, 552–565.
3 Lu, Rencai; Zhao, Kaiming; Classification of irreducible weight modules over higher rank Virasoro algebras. Adv. Math. 206 (2006), no. 2, 630–656.
2 Lü, Rencai; Tang, Zhongming; The f-depth of an ideal on a module. Proc. Amer. Math. Soc. 130 (2002), no. 7, 1905–1912.
1 Lü, Rencai; Zhao, Kaiming; Automorphism groups of Weyl-type algebras. Manuscripta Math. 107 (2002), no. 2, 207–214.
教育及工作经历
2007- 苏州大学数学科学学院
2005-2007 中科院数学所博士后
2003-2005 北京大学数学学院博士后
2000-2003 中科院系统所博士
1993-2000 苏州大学数学学院本科、硕士研究生
研究方向
主要从事李代数的研究工作。先后主持国家自然科学基金项目3项，参与3项. 在Advances in Mathematics, Documenta Mathematica, Journal of Algebra, Communications in Contemporary Mathematics等SCI杂志上发表学术论文30余篇。
41 Hu, jinxin; Lü, Rencai; Classification of simple Harish-Chandra modules of the Cartan type Lie algebra \bar{S}_2， to appear in J. Algebra.
40 Y. Cai, R.Lü ,X. Wang, Non-weight modules over the Lie (super)algebras related to the Virasoro algebra, J. Algebra {\bf 683} (2025), 834--857; MR4936484
39 Yan-an Cai;Rencai Lü;Yaohui Xue;Classification of Simple Strong Harish-Chandra Modules Over the Lie Superalgebra of Vector Fields on $C^{m|n}$, to appear in Transformation Groups.
38 R. Lü, Y. Xue, Classification of simple Harish-Chandra modules over the generalized Witt algebras, J. Algebra {\bf 650} (2024), 54--79; MR4733241
37 Y. Cai, Y. He ,R. Lü, Module structures on U(S^-) for the Schr\"odinger algebra, J. Geom. Phys. {\bf 191} (2023), Paper No. 104919, 8 pp.; MR4618896
36 Lü, Rencai; Xue, Yaohui;Bounded weight modules over the Lie superalgebra of Cartan W-type, Algebr. Represent. Theory 26 (2023), no. 3, 763–781.
35 Xue, Yaohui; Lü, Rencai; Classification of simple bounded weight modules of the Lie algebra of vector fields on $\bC^n$, Israel J. Math. 253 (2023), no. 1, 445–468.
34 Cai, Yan-an, Lü, Rencai, Classification of simple Harish-Chandra modules over the Neveu-Schwarz algebra and its contact algebra, J. Pure Appl. Algebra 226 (2022), no. 3, Paper No. 106866, 14 pp.
33 Xue, Yaohui; Lü, Rencai;Simple weight modules with finite-dimensional weight spaces over Witt superalgebras, J. Algebra 574(2021), 92-116.
32 Cai, Yan-an; Lü, Rencai; Wang,Yan; Classification of simple Harish-Chandra modules for map (super)algebras related to the Virasoro algebra, Journal of Algebra, 570(2021),397-415
31 Cai, Yan-an; Liu, Dong; Lü, Rencai; Classification of simple Harish-Chandra modules over the N = 1 Ramond algebra, Journal of Algebra Volume 567(2021),114-127
30 Lü, Rencai; Zhao, Kaiming Generalized oscillator representations of the twisted Heisenberg-Virasoro algebra. Algebr. Represent. Theory 23 (2020), no. 4, 1417–1442.
29 Guo, Xiangqian; Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; Simple Witt modules that are finitely generated over the Cartan subalgebra. Mosc. Math. J. 20 (2020), no. 1, 43–65.
28 He, Yan; Cai, Yan-an; Lü, Rencai; A class of new simple modules for sln+1 and the Witt algebra. J. Algebra 541 (2020), 415–435.
27 Brešar, Matej; Guo, Xiangqian; Liu, Genqiang; Lü, Rencai; Zhao, Kaiming; Zero product determined Lie algebras. Eur. J. Math. 5 (2019), no. 2, 424–453.
26 Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; Irreducible Witt modules from Weyl modules and gln-modules. J. Algebra 511 (2018), 164–181.
25 Futorny, Vyacheslav; Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; New families of irreducible weight modules over sl3. J. Algebra 501 (2018), 458–472.
24 Cox, Ben; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Simple superelliptic Lie algebras. Commun. Contemp. Math. 19 (2017), no. 3, 1650032, 22 pp.
23 Lü, Rencai; Zhao, Kaiming; A family of simple weight modules over the Virasoro algebra. J. Algebra 479 (2017), 437–460.
22 Adamović, Dražen; Lü, Rencai; Zhao, Kaiming; Whittaker modules for the affine Lie algebra A(1)1. Adv. Math. 289 (2016), 438–479.
21 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Classification of simple weight modules over the 1-spatial ageing algebra. Algebr. Represent. Theory 18 (2015), no. 2, 381–395.
20 Lü, Rencai; Zhao, Kaiming; Finite-dimensional simple modules over generalized Heisenberg algebras. Linear Algebra Appl. 475 (2015), 276–291.
19 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Simple weight modules over weak generalized Weyl algebras. J. Pure Appl. Algebra 219 (2015), no. 8, 3427–3444.
18 Liu, Genqiang; Lu, Rencai; Zhao, Kaiming; A class of simple weight Virasoro modules. J. Algebra 424 (2015), 506–521.
17 Dubsky, Brendan; Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; Category O for the Schrödinger algebra. Linear Algebra Appl. 460 (2014), 17–50.
16 Lu, Rencai; Zhao, Kaiming; Irreducible Virasoro modules from irreducible Weyl modules. J. Algebra 414 (2014), 271–287.
15 Cox, Ben; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; n-point Virasoro algebras and their modules of densities. Commun. Contemp. Math. 16 (2014), no. 3, 1350047, 27 pp.
14 Lü, Rencai; Mazorchuk, Volodymyr; Zhao, Kaiming; On simple modules over conformal Galilei algebras. J. Pure Appl. Algebra 218 (2014), no. 10, 1885–1899.
13 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Fraction representations and highest-weight-like representations of the Virasoro algebra. J. Algebra 387 (2013), 68–86.
12 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras. Proc. Edinb. Math. Soc. (2) 55 (2012), no. 3, 697–709.
11 Lü, Rencai; Guo, Xiangqian; Zhao, Kaiming; Irreducible modules over the Virasoro algebra. Doc. Math. 16 (2011), 709–721.
10 Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra. Forum Math. 23 (2011), no. 5, 1029–1052.
9 Lü, Rencai; Zhao, Kaiming; Classification of irreducible weight modules over the twisted Heisenberg-Virasoro algebra. Commun. Contemp. Math. 12 (2010), no. 2, 183–205.
8 Lü, Rencai; Zhao, Kaiming; Verma modules over quantum torus Lie algebras. Canad. J. Math. 62 (2010), no. 2, 382–399.
7 Batra, Punita; Guo, Xiangqian; Lu, Rencai; Zhao, Kaiming; Highest weight modules over pre-exp-polynomial Lie algebras. J. Algebra 322 (2009), no. 12, 4163–4180.
6 Lü, RenCai; Weight modules over some Block algebras. Sci. China Ser. A 52 (2009), no. 3, 517–525.
5 Lü, Rencai; Classification of quasifinite modules with nonzero central charges for EALAs of Type A with coordinates in quantum torus. Chin. Ann. Math. Ser. B 30 (2009), no. 2, 129–138.
4 Lü, Rencai; Zhao, Kaiming; Structure of Weyl type Lie algebras. J. Algebra 306 (2006), no. 2, 552–565.
3 Lu, Rencai; Zhao, Kaiming; Classification of irreducible weight modules over higher rank Virasoro algebras. Adv. Math. 206 (2006), no. 2, 630–656.
2 Lü, Rencai; Tang, Zhongming; The f-depth of an ideal on a module. Proc. Amer. Math. Soc. 130 (2002), no. 7, 1905–1912.
1 Lü, Rencai; Zhao, Kaiming; Automorphism groups of Weyl-type algebras. Manuscripta Math. 107 (2002), no. 2, 207–214.