吴泉水
非交换环论、非交换射影代数几何、Hopf代数的同调理论
个性化签名
- 姓名:吴泉水
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学术头衔:
博士生导师
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学科领域:
数理逻辑与数学基础
- 研究兴趣:非交换环论、非交换射影代数几何、Hopf代数的同调理论
吴泉水,1984年12月获武汉大学数学系基础数学专业硕士学位。1987年2月获复旦大学数学研究所基础数学专业博士。曾先后赴美国华盛顿大学、德国慕尼黑大学、以色列海法大学访问学习。多次应邀访问美国、德国、比利时、意大利、英国等国家的多所大学;多次在国内外学术会议上作大会报告。已在Trans. AMS,J. Algebra 等学术刊物上发表论文20余篇。 在非交换环论、非交换射影代数几何、Hopf代数的同调理论方面作出过高质量的研究工作。曾获教育部科技进步二等奖(第二获奖人);上海市优秀青年教师称号;教育部霍英东教育基金会青年教师奖;教育部第四届高校“青年教师奖”等。
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主页访问
2589
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关注数
1
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成果阅读
233
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成果数
6
【期刊论文】HOMOLOGICAL INTEGRAL OF HOPF ALGEBRAS
吴泉水, D.-M. LU, Q.-S. WU AND J.J. ZHANG
,-0001,():
-1年11月30日
The left and right homological integrals are introduced for a large class of infinite dimensional Hopf algebras. Using the homological integrals we prove a version of Maschke's theorem for infinite dimensional Hopf algebras. The generalization of Maschke's theorem and homological integrals are the keys to study noetherian regular Hopf algebras of Gelfand-Kirillov dimension one.
Hopf algebra,, homological integral,, Gorenstein property,, regularity,, Gelfand-Kirillov dimension,, integral order,, integral quotient,, PI degree.,
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【期刊论文】Regularity of involutory PI Hopf algebras
吴泉水, Q.-S. Wu a, and J.J. Zhang b, *,
Journal of Algebra 256 (2002) 599-610,-0001,():
-1年11月30日
Let H be an involutory Hopf algebra over a field of characteristic 0. If H is either a finite module over its affine center or a semiprime noetherian affine PI algebra, then it is Auslander regular and Cohen-Macaulay and is a finite direct sum of prime rings.
Hopf algebra, Global dimension
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39浏览
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【期刊论文】Homological Identities for Noncommutative Rings
吴泉水, Q.-S. Wu, J.J. Zhang
Journal of Algebra 242, 516-535 (2001),-0001,():
-1年11月30日
The Auslander–Buchsbaum formula and Bass's theorem are proved for a class of nonlocal, noncommutative algebras (including certain affine PI Hopf algebras). We also show that each filtered noetherian affine PI Hopf algebra has finite injective dimension, which partially answers a question of Brown.
Auslander-Buchsbaum formula, Bass', s theorem, AS-Gorensteinness, Hopf algebra.,
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【期刊论文】Dualizing Complexes over Noncommutative Local Rings
吴泉水, Q.-S. Wu, J.J. Zhang
Journal of Algebra 239, 513-548 (2001),-0001,():
-1年11月30日
We prove an existence theorem for dualizing complexes over noncommutative noetherian complete semilocal algebras, which generalizes Van den Bergh's existence theorem in the graded case. Using the dualizing complex, noncommutative versions of Bass theorem and the no-holes theorem are proved. We also prove that noetherian complete semilocal algebras satisfying polynomial identities are catenary.
semilocal algebra, PI algebra, local cohomology, dualizing complex, Bass theorem, no-holes theorem
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【期刊论文】Some Homological Invariants of Local PI Algebras
吴泉水, Q.S. Wu, J.J. Zhang
Journal of Algebra 225, 904-935 (2000),-0001,():
-1年11月30日
semilocal PI algebra, Auslander-Buchsbaum formula, depth, local cohomology, Morita duality.,
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