ON q-SKEW ITERATED ORE EXTENSIONS SATISFYING A POLYNOMIAL IDENTITY

Abstract

For iterated Ore extensions satisfying a polynomial identity we present an elementary way of erasing derivations. As a consequence we recover some results obtained by Haynal in [5]. We also prove, under mild assumptions on R n = R[x 1

Dipper Donkin Quantized Matrix Algebra and Reflection Equation Algebra at root of unity

“…For that it is enough to show that the first equality is valid for arbitrary characteristic. Here we will use another derivation erasing process (independent of characteristic) duo to Leroy and Matczuk as in [11,Theorem 7]. We define an ordering on the set of generators , 1 ≤ , ≤ of Mat ( ) by lexicographic ordering on the set of indices.…”

On the importance of being primitive

“…One of the amazing features of CGL extensions, despite the fact that they involve both automorphisms and σ-derivations, is that, for the purposes of understanding their spectra, one can pass to the pure automorphism case via the so-called deleting derivations algorithm, which was first given by Cauchon [Cau03]; the main idea behind this algorithm is that by passing to a suitable localization one can show that the resulting algebra is isomorphic to a skew polynomial algebra in which one has only automorphisms and no derivations; then, by working backwards, one can reconstruct the spectrum in a step-by-step manner. This, in particular, has allowed one to go in many cases well beyond the understanding of the prime and primitive spectrum affording by knowing the Dixmier-Moeglin equivalence and this technique has since been used to great effect by numerous authors-for a small sample, see [Cas14,GLL11,LM11,Yak10,Yak14].…”

Twist invariants of graded algebras

“…Proof. It is well known that O q (K n ) is a PI algebra if and only if all q ij are roots of unity (e.g., [14,Theorem 7]), i.e., if and only if q is finite. which is a multiplicatively skew-symmetric matrix, and…”

“…Proof. It is well known that O q (K n ) is a PI algebra if and only if all q ij are roots of unity (e.g., [14,Theorem 7]), i.e., if and only if q is finite. The inequality in Corollary 4.2 is by no means sharp, as can be seen from the formula for PI-deg O q (K n ) in [7, Proposition 7.1(c)].…”