Details:
Title  Noncommutative Grobner Bases for Almost Commutative Algebras  Author(s)  Huishi Li  Type  Technical Report, Misc  Abstract  Let $K$ be an infinite field and $K< X> =K< X_1,...,X_n>$ the free associative algebra generated by $X=\{X_1,...,X_n\}$ over $K$. It is proved that if $I$ is a twosided ideal of $K< X>$ such that the $K$algebra $A=K< X> /I$ is almost commutative in the sense of [3], namely, with respect to its standard $\mathbb{N}$filtration $FA$, the associated $\mathbb{N}$graded algebra $G(A)$ is commutative, then $I$ is generated by a finite Gr\"obner basis. Therefor, every quotient algebra of the enveloping algebra $U(\mathbf{g})$ of a finite dimensional $K$Lie algebra $\mathbf{g}$ is, as a noncommutative algebra of the form $A=K< X> /I$, defined by a finite Gr\"obner basis in $K< X>$.
 Keywords  Allmost commutative algebra, Filtration, Gradation, Groebner basis  Length  7 
File 
 URL 
http://arxiv.org/pdf/math/0701120 
Language  English  Year  2007  Month  January  Edition  0  Translation 
No  Refereed 
No 
