Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras

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Standard

Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. / Hartwig, J.T. ; Öinert, Per Johan.

I: Journal of Algebra, Bind 373, 2013, s. 312-339.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Hartwig, JT & Öinert, PJ 2013, 'Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras', Journal of Algebra, bind 373, s. 312-339. https://doi.org/10.1016/j.jalgebra.2012.10.009

APA

Hartwig, J. T., & Öinert, P. J. (2013). Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. Journal of Algebra, 373, 312-339. https://doi.org/10.1016/j.jalgebra.2012.10.009

Vancouver

Hartwig JT, Öinert PJ. Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. Journal of Algebra. 2013;373:312-339. https://doi.org/10.1016/j.jalgebra.2012.10.009

Author

Hartwig, J.T. ; Öinert, Per Johan. / Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras. I: Journal of Algebra. 2013 ; Bind 373. s. 312-339.

Bibtex

@article{29a5e5df155043ca82b1613815e9b078,
title = "Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras",
abstract = "In this paper we prove three theorems about twisted generalized Weyl algebras (TGWAs). First, we show that each non-zero ideal of a TGWA has non-zero intersection with the centralizer of the distinguished subalgebra R . This is analogous to earlier results known to hold for crystalline graded rings. Second, we give necessary and sufficient conditions for the centralizer of R to be commutative (hence maximal commutative), generalizing a result by V. Mazorchuk and L. Turowska. And third, we generalize results by D.A. Jordan and V. Bavula on generalized Weyl algebras by giving necessary and sufficient conditions for certain TGWAs to be simple, in the case when R is commutative. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples. We also discuss how simplicity of a TGWA is related to the maximal commutativity of R and the (non-)existence of non-trivial Zn-invariant ideals of R.",
author = "J.T. Hartwig and {\"O}inert, {Per Johan}",
year = "2013",
doi = "10.1016/j.jalgebra.2012.10.009",
language = "English",
volume = "373",
pages = "312--339",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Simplicity and maximal commutative subalgebras of twisted generalized Weyl algebras

AU - Hartwig, J.T.

AU - Öinert, Per Johan

PY - 2013

Y1 - 2013

N2 - In this paper we prove three theorems about twisted generalized Weyl algebras (TGWAs). First, we show that each non-zero ideal of a TGWA has non-zero intersection with the centralizer of the distinguished subalgebra R . This is analogous to earlier results known to hold for crystalline graded rings. Second, we give necessary and sufficient conditions for the centralizer of R to be commutative (hence maximal commutative), generalizing a result by V. Mazorchuk and L. Turowska. And third, we generalize results by D.A. Jordan and V. Bavula on generalized Weyl algebras by giving necessary and sufficient conditions for certain TGWAs to be simple, in the case when R is commutative. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples. We also discuss how simplicity of a TGWA is related to the maximal commutativity of R and the (non-)existence of non-trivial Zn-invariant ideals of R.

AB - In this paper we prove three theorems about twisted generalized Weyl algebras (TGWAs). First, we show that each non-zero ideal of a TGWA has non-zero intersection with the centralizer of the distinguished subalgebra R . This is analogous to earlier results known to hold for crystalline graded rings. Second, we give necessary and sufficient conditions for the centralizer of R to be commutative (hence maximal commutative), generalizing a result by V. Mazorchuk and L. Turowska. And third, we generalize results by D.A. Jordan and V. Bavula on generalized Weyl algebras by giving necessary and sufficient conditions for certain TGWAs to be simple, in the case when R is commutative. We illustrate our theorems by considering some special classes of TGWAs and providing concrete examples. We also discuss how simplicity of a TGWA is related to the maximal commutativity of R and the (non-)existence of non-trivial Zn-invariant ideals of R.

U2 - 10.1016/j.jalgebra.2012.10.009

DO - 10.1016/j.jalgebra.2012.10.009

M3 - Journal article

VL - 373

SP - 312

EP - 339

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 113989408