Timeline for Normal regular sequence in noncommutative algebras

7 events

when toggle format	what		by	license	comment
Nov 2, 2015 at 6:49	vote	accept	Leslie Wu
Jun 18, 2013 at 14:32	answer	added	Vladimir Dotsenko		timeline score: 2
Jun 18, 2013 at 12:50	answer	added	J. Gaddis		timeline score: 1
May 13, 2013 at 2:35	comment	added	Leslie Wu		I am more interested in this question: given $\{ a, b\} $ in $k_q[x, y]$ where $q^n = 1$, what are the characteristics of such pair $\{ a, b\}$?. This question is much easier in the commutative case, that is, the polynomial ring with two variables, where we can say two elements $\{ f, g\}$ in $k[x, y]$ are regular sequence if and only if gcd$(f, g) = 1$ if and only if $\dim_k k[x, y]/(f, g) < \infty$. I am expecting an analogue in the noncommutative case, more specifically, in the quantum plane $k_q[x, y]$ where $q$ is not generic.
May 13, 2013 at 2:29	comment	added	Leslie Wu		The result I referred to is as follows: Let $A$ be locally finite graded $k$-algebra. Let $x_1, \ldots, x_n$ be a normal sequence of homogeneous elements with deg$(x_i) = d_i$. Then $\{ x_1, \ldots, x_n\}$ is a regular sequence if and only if the Hilbert polynomials of $A$ and $A/(x_1, \ldots, x_n)$ satisfy $$ H_{A/(x_1, \ldots, x_n)} (t) = \Pi_{i=1}^n (1 - t^{d_i}) H_A(t).$$
May 12, 2013 at 5:14	comment	added	Mariano Suárez-Álvarez		If you explained what is that «some result» in the homogeneous case, it might be easier to see what you are after in the general case.
May 12, 2013 at 4:39	history	asked	Leslie Wu	CC BY-SA 3.0