ABSTRACT This paper deals with the application of methods stemming from computational commutative... more ABSTRACT This paper deals with the application of methods stemming from computational commutative algebra to some quantum groups (Weyl algebras, enveloping algebra of a finite dimensional Lie algebra...), using the fact that most quantum groups have PBW-bases
We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodul... more We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodules,} {\em Tsukuba J. Math.} \textbf{13} (1989), 353--362) which proposes a non-commutative version of the fact that for a faithfully flat extension of commutative rings $R \subseteq S$, the relative Picard group $Pic(S/R)$ is isomorphic to the Amitsur 1--cohomology group $H^1(S/R,U)$ with coefficients in the units functor $U$.
Proceedings of the Edinburgh Mathematical Society, 1997
In this note we propose an effective method based on the computation of a Gröbner basis of a left... more In this note we propose an effective method based on the computation of a Gröbner basis of a left ideal to calculate the Gelfand-Kirillov dimension of modules.
We introduce the notion of right strictly quasi-finite coalgebras, as coalgebras with the propert... more We introduce the notion of right strictly quasi-finite coalgebras, as coalgebras with the property that the class of quasi-finite right comodules is closed under factor comodules, and study its properties. A major tool in this study is the local techniques, in the sense of abstract localization.
In [1], K. R. Goodearl and E. S. Letzter study prime and primitive ideals in certain iterated Ore... more In [1], K. R. Goodearl and E. S. Letzter study prime and primitive ideals in certain iterated Ore extensions of an infinite field k of arbitrary characteristic, which include several quantized algebras at non roots of unity, among them the quantized algebras Oqðspk Þ of symplectic spaces. The general framework to work in is to consider some group H acting as automorphism on a ring R which give the set H SpecðRÞ consisting of all H-prime ideals of R. The H-stratification of the prime spectrum SpecðRÞ is then defined as
ABSTRACT This paper deals with the application of methods stemming from computational commutative... more ABSTRACT This paper deals with the application of methods stemming from computational commutative algebra to some quantum groups (Weyl algebras, enveloping algebra of a finite dimensional Lie algebra...), using the fact that most quantum groups have PBW-bases
We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodul... more We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodules,} {\em Tsukuba J. Math.} \textbf{13} (1989), 353--362) which proposes a non-commutative version of the fact that for a faithfully flat extension of commutative rings $R \subseteq S$, the relative Picard group $Pic(S/R)$ is isomorphic to the Amitsur 1--cohomology group $H^1(S/R,U)$ with coefficients in the units functor $U$.
Proceedings of the Edinburgh Mathematical Society, 1997
In this note we propose an effective method based on the computation of a Gröbner basis of a left... more In this note we propose an effective method based on the computation of a Gröbner basis of a left ideal to calculate the Gelfand-Kirillov dimension of modules.
We introduce the notion of right strictly quasi-finite coalgebras, as coalgebras with the propert... more We introduce the notion of right strictly quasi-finite coalgebras, as coalgebras with the property that the class of quasi-finite right comodules is closed under factor comodules, and study its properties. A major tool in this study is the local techniques, in the sense of abstract localization.
In [1], K. R. Goodearl and E. S. Letzter study prime and primitive ideals in certain iterated Ore... more In [1], K. R. Goodearl and E. S. Letzter study prime and primitive ideals in certain iterated Ore extensions of an infinite field k of arbitrary characteristic, which include several quantized algebras at non roots of unity, among them the quantized algebras Oqðspk Þ of symplectic spaces. The general framework to work in is to consider some group H acting as automorphism on a ring R which give the set H SpecðRÞ consisting of all H-prime ideals of R. The H-stratification of the prime spectrum SpecðRÞ is then defined as
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