Discriminants and automorphism groups of Veronese subrings of skew polynomial rings

Abstract. A noncommutative analogue of the Zariski cancellation problem asks whether A[x] ∼ = B[x] implies A ∼ = B when A and B are noncommutative algebras. We resolve this affirmatively in the case when A is a noncommutative finitely generated domain over the complex field of Gelfand-Kirillov dimension two. In addition, we resolve the Zariski cancellation problem for several classes of Artin-Schelter regular algebras of higher Gelfand-Kirillov dimension.

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“…We say a normal element x ∈ B is the greatest common divisor or gcd Some explicit examples of discriminants are given in [CPWZ1,CPWZ2,CYZ1,CYZ2].…”

Section: Discriminantmentioning

confidence: 99%

Zariski cancellation problem for noncommutative algebras

Bell

Zhang

2017

Sel. Math. New Ser.

121

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“…The above lemma provides a lot of examples that are strongly retractable. We refer to papers [BZ1,CPWZ1,CPWZ2,CYZ2,LY] for many examples that are strongly LND-rigid or strongly LND H -rigid.…”

Section: Lnd Z -Rigidity Controls Retractabilitymentioning

confidence: 99%

“…This paper can be considered as a sequel to [BZ1], where Bell-Zhang studied Zariski Cancellation Problem for noncommutative domains (in particular, for several families of Artin-Schelter regular algebras [AS]). Many mathematicians have been making significant contributions to this research direction and related topics, see Brown-Yakimov [BY], Ceken-Palmieri-Wang-Zhang [CPWZ1,CPWZ2], Chan-Young-Zhang [CYZ1,CYZ2], Gaddis [Ga], Gaddis-Kirkman-Moore [GKM], Gaddis-Won-Yee [GWY], Levitt-Yakimov [LY], Lü-Mao-Zhang [LMZ], Nguyen-Trampel-Yakimov [NTY], Tang [Ta1,Ta2] and others.…”

Section: Introductionmentioning

confidence: 99%

Zariski cancellation problem for non-domain noncommutative algebras

2018

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“…Recently, the study of cancellation problem has been revitalized for noncommutative algebras thanks to [BZ1], which mainly employs the famous Makar-Limanov invariants [Ma1,Ma2] and the noncommutative discriminants as investigated in [CPWZ1,CPWZ2]. It is usually very difficult to describe the discriminant for a given algebra; fortunately, many useful results on discriminants have been further established in [BY,CYZ1,CYZ2,GKM,GWY,NTY,WZ]. Ever since [BZ1], there has been much progress made in the study of cancellation problem for noncommutative algebras [BZ2,CYZ1,Ga,LR,LY,LeWZ,LuWZ,LMZ,Ta1,Ta2,TRZ].…”

Section: Introductionmentioning

confidence: 99%