We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.展开更多
In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-inject...In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.展开更多
Let A be a connected minimal representation-infinite algebra over an alge- braically closed field k. In this paper, we investigate the simple connectedness and strong simple connectedness of A. We prove that A is simp...Let A be a connected minimal representation-infinite algebra over an alge- braically closed field k. In this paper, we investigate the simple connectedness and strong simple connectedness of A. We prove that A is simply connected if and only if its first Hochschild cohomology group Hi （A） is trivial. We also give some equivalent conditions of strong simple connectedness of an algebra A.展开更多
We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other re...We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other regularization schemes given in the literature.展开更多
We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmoni...We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors展开更多
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.
基金supported by the National Natural Science Foundation of China(11671230,11371165).
文摘In this article we investigate the relations between the Gorenstein projective dimensions of Λ-modules and their socles for re-minimal Auslander-Gorenstein algebras Λ.First we give a description of projective-injective Λ-modules in terms of their socles.Then we prove that a Λ-module N has Gorenstein projective dimension at most n if and only if its socle has Gorenstein projective dimension at most n if and only if N is cogenerated by a projective Λ-module.Furthermore,we show that n-minimal Auslander-Gorenstein algebras can be characterised by the relations between the Gorenstein projective dimensions of modules and their socles.
基金Supported by the National Natural Science Foundation of China （grant No. 10371036 11271119） and the Natural Science foundation of Beijing （grant No. 1122002）.Acknowledgement. The authors would like to express their gratitude to the referee（s） for helpful comments and valuable suggestions.
文摘Let A be a connected minimal representation-infinite algebra over an alge- braically closed field k. In this paper, we investigate the simple connectedness and strong simple connectedness of A. We prove that A is simply connected if and only if its first Hochschild cohomology group Hi （A） is trivial. We also give some equivalent conditions of strong simple connectedness of an algebra A.
文摘We renormalize the model of multiple Dirac delta potentials in two and three dimensions by regularizing it through the minimal extension of Heisenberg algebra. We show that the results are consistent with the other regularization schemes given in the literature.
基金Supported by National Natural Science Foundation of China(Grant No.11171324)
文摘We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl（n,F）-modules that appeared in the Z2-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.Service E-mail this articleAdd to my bookshelfAdd to citation managerE-mail AlertRSSArticles by authors
