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 two-sided 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