章璞
章璞,男,1962年6月出生,安徽省金寨县人。现任中国科学技术大学数学系教授,博导。主要从事代数学的教学和研究。
主讲过的本科生和研究生课程:微积分,线性代数,近世代数,同调代数,群表示论,代数表示论,Lie代数,Hopf代数,Hall代数,量子群,及代数数论。
主要研究方向:代数与群的表示,Auslander-Reiten理论,Hochschild上同调群,Koszul代数,Ringel-Hall代数与量子群,拟遗传代数,Lie理论,Hopf代数,已完成论文50余篇,其中47篇已发表.
曾在德国做 Humboldt 及 Volkswagen 学者,美国做 Visiting Professor。访问过加拿大,挪威,比利时,巴西,韩国,新加坡, 英国及香港等地的大学和研究所。
任印度"Far East J. of Math. Science" 编委(web site:http://www.pphmj.com),
美国"Math. Review" 评论员及美国数学会会员。
I. 在研项目
参加万哲先院士主持的国家自然科学基金重点项目
“代数学中的组合方法”(10301033, 2004.1-2007.12)
主持国家自然科学基金面上项目
“斜微分算子代数在表示论和量子群中的应用”(10271113, 2003.1-2005.12)
主持教育部博士点基金
“有限域上的表示论”(2003.1-2005.12)
参加C.M.Ringel教授主持的德国大众汽车国际合作项目“Dastellungstheorie Von Algebren”、
F.van Oystaeyen教授主持的比利时Flemish双边合作项目“Quantum groups and differential operators"
S.Koenig教授主持的欧盟国际合作项目“Algebras and Representations in China and Europe”
和Leverhulme Network "Algebras, Representations, and Applications".
II. 已发表的论文
48. Skew differential operator algebras of twisted Hopf algebras
Advances in Mathematics 183(1)(2004), 80-126. (美国, SCI)
47. Monomial Hopf algebras (与陈小伍、黄华林、叶郁合作)
J.Algebra 275(2004), 212-232. (美国, SCI)
46. Koszul modules and modules with linear presentations
(与E. L. Green and E. Marcos合作),
Comm. Algebra 31(6)(2003), 2745-2770. (美国, SCI)
45. Finite groups with grahps containing no triangles (与方明合作)
J. Algebra 264(2003), 613-619. (美国, SCI)
44. Quivers and Hopf algebras (与Fred van Oystaeyen合作)
In: Nonlinear evolution equations and Dynamical systems, Proc. ICM 2002 Satellite
Conf., World Scientific, 2003, 121-134.
43. Generalized Green's classes
J. Algebra 250(2002), 709-730. (美国, SCI)
42. Higher Koszul modules (与叶郁合作)
中国科学(A)(32)(11)(2002), 1042-1049. (中国, SCI)
41. Higher Koszul complexes (与叶郁合作)
中国科学(A)(32)(9)(2002), 819-829. (中国, SCI)
40. Triangular decomposition of affine composition algebras (与黄华林合作)
Chinese J. Contemp. Math. 23(2)(2002),137-147.(中国数学年刊英文版)
39. Colored Ringel-Hall algebras: Applications to quantized Borcherds superalgebras
(与李立斌合作), Proc. 9-th Inter. Conf. Rep. alg. (Editors:
D.Happel, 张英伯), 北京师范大学出版社, 2002, 308-320. (北京国际会议论文集)
38. Minimal generators of Ringel-Hall algebras of affine quivers (与张英伯,郭晋云合作)
J. Algebra 239(2001), 675-704. (美国, SCI)
37. Weight property for ideals of U_q(sl_2) (与李立斌合作)
Comm. in Algebra 29(11)(2001), 4853-4870. (美国, SCI)
36. Twisted Hopf algebras (与李立斌合作)
In: Representations of Algebras
Proc. International Conf. on Algebra in Sao Paulo, Brazil
Lecture Notes in Pure and Applied Mathematics, Vol. 224 (2002), 269-282
Marcel Dekker, Inc. New York, Basel. (巴西国际会议论文集)
35. Representations as elements in affine composition algebras
Trans. Amer. Math. Soc. 353(3)(2001), 1221-1249. (美国, SCI)
34. Infinite quivers and cohomology groups
In: Trends in Mathematics
Proc. International Symposium on Ring Theory, Kyongju, South Korea, 1999
Published by Birkhause, Boston, 2001, 427-440. (韩国国际会议论文集)
33. Quantum adjoint actions for U_q(sl_2)(与李立斌合作)
Algebra Colloquium 7:4(2000), 363-379. (中国, SCI)
32. Vanishing of the first Hochschild cohomology
In: Proc. International Conf. on Representation Theory in Shanghai
Published by 高等教育-Springer 出版社, 421-428, 2000. (上海国际会议论文集)
31. PBW-basis of the composition algebra of the Kronecker algebra
J. reine angew. Math. 527(2000), 97-116. (德国, SCI)
30. Twisted Hopf algebras, Ringel-Hall algebras, and Green's classes (与李立斌合作)
J. Algebra 231(2000), 713-743. (美国, SCI)
29. Indecomposables in the composition algebra of the Kronecker algebra
Comm. in Algebra 27(10)(1999), 4633-4639. (美国, SCI)
28. O-algebras with three simple modules
J. Pure Applied Algebra 142(1999), 183-197.(荷兰, SCI)
27. Indecomposables as elements in affine composition algebras (与张顺华合作)
J. Algebra 210(1998), 614-629. (美国, SCI)
26. Composition algebras of affine type
J. Algebra 206 (1998), 505-540. (美国, SCI)
25. The Hochschild homology of a truncated basic cycle
Algebra Colloquium 5:1(1998), 77-84. (中国, SCI)
24. Selforthogonal radical algebras
In: Canadian Math. Soc. Conf. Proc. 24 (1998), 563-569
Published by Amer.Math.Soc.-Canad.Math.Soc.(加拿大国际会议论文集)
23. A criterion of quasi-heredity and the characteristic modules
Manuscripta Math. 93(1997), 129-135. (德国, SCI)
22. An equality on Hochschild homology (与刘绍学合作)
科学通报 42(8)(1997), 624-627.(中国, SCI)
21. Ringel - Hall algebras of standard homogeneous tubes
Algebra Colloquium 4:1 (1997), 89-94. (中国, SCI)
20. Characteristic modules of quasi-hereditary algebras with three simples
(与林亚南合作), 科学通报 42(6)(1997), 450-453. (中国, SCI)
19. Hochschild cohomology of a truncated basic cycle
中国科学 (A)40(12)(1997), 1272-1278. (中国, SCI)
18. Triangular decomposition of the composition algebra of the Kronecker algebra
J. Algebra 184 (1996), 159-174. (美国, SCI)
17. Quasi-hereditary algebras and tilting modules
Comm. in Algebra 24(12) 1996, 3707-3717. (美国, SCI)
16. Representation theory of finite-dimensional algebras in China (与刘绍学合作)
In: Lecture Notes in Pure and App. Math. Vol. 181 (1996), 159-179
Published by Marcel Dekker Inc., New York, Basel. (论文集)
15. 截面代数的Hochschild上同调群
中国科学 (A) 24(11)(1994), 1121-1125.
14. 弱直向代数的Hochschild上同调群
科学通报 39(22)(1994), 2025-2027.
13. Hochschild homology of truncated algebras (与刘绍学合作)
Bull. London Math. Soc. 26(1994), 427-430. (英国, SCI)
12. One class of representations of trivial extensions of iterated tilted alg.
(与肖杰合作), Tsukuba J. Math. 17(1)(1993), 131-141. (日本)
11. On the Hochschild homology groups of some finite dimensional algebras
(与刘绍学合作), In: Canadian Math. Soc.Conf. Proc. 14(1993), 353-360.
Published by Amer. Math. Soc.- Canad. Math. Soc. (加拿大国际会议论文集)
10. Directing components of Auslander-Reiten quivers
中国科学 (A)(36)(1993), 265-274. (中国, SCI)
9. Some results concerning wild tilted algebras
In: Proc. of the First China - Japan - Korea International Conf. on Ring Theory
Published by Okayama University Press, Japan, (1992) 180-182. (中日韩国际会议论文集)
8. 倾斜代数的Auslander-Reiten序列
数学季刊 3(1992), 58-65.
7. Endomorphism algebras of preprojective partial tilting modules
科学通报 37(22)(1992), 1857-1860.
6. Separating tilting modules
科学通报 37(12)(1992),975-978.
5. 倾斜代数的一类单点扩张(I)
数学学报 34(5)(1991), 710-717.
4. 倾斜代数的一类单点扩张(II)
数学学报 34(4)(1991), 566-574.
3. 半单算子与半单类
数学杂志 10(2)(1990), 145-149.
2. 环的$(k,l,m,n)-根(与蔡传仁合作)
数学研究与评论 9(2)(1989), 207-210.
1. 根类的极小生成子
扬州师范学院学报 9(2)(1989), 7-10.
III. 已接受发表或已完成的论文
55. Rigids as iterated skew commutators of simples (与E.L. Green合作)
Algebras and Representation Theory (已接受发表). (荷兰, SCI)
54. D-Koszul algebras (与E.L. Green, E. Marcos, R. Martinez-Villa合作),
J. Pure Appl. Algebra (已接受发表). (荷兰, SCI).
53. Generalized Taft's algebras (与黄华林,陈惠香合作)
Algebra Colloquium (已接受发表). (中国, SCI)
52. Construct biFrobenius algebras via quivers (与王艳华合作)
Tsukuba J. Math.(已接受发表).(日本)
51. Quiver Hopf algebras (与F.van Oystaeyen合作), preprint.
50. Dual Gabriel theorem with applications (与陈小伍、黄华林),preprint
49. Comudule Hopf algebras over CQT bialgebras (与孙建华合作), prepint.
IV. 所著讲义
1. Lecture Notes on Ringel-Hall algebras and quantum groups, preprint.
2. Lecture Notes on Hochschild cohomology groups, preprint.
3. 群与代数表示引论, (与冯克勤、李尚志合作), 中国科学技术大学出版社 2003.
4. Lecture Notes on Quivers and Hopf Algebras (与F.van Oystaeyen合作), preprint.
5. 计算代数讲义, (与冯克勤、李尚志合作), preprint.