Ergodipotent maps and commutativity of elements in noncommutative rings and algebras with twisted intertwining
(2007) In Journal of Algebra 314(1). p.17-41- Abstract
- A property of algebraic dependence between two commuting elements is shown to hold in a more general setting than that in which it has previously been established. Key conditions are identified and some methods for establishing them are given. Moreover the class of algebras with a generalised Weyl structure, generalising the so-called Generalised Weyl Algebras (GWAs) or hyperbolic rings, is introduced and studied. We also present an interesting class of algebras which are not GWAs but share many of their properties by virtue of their generalised Weyl structure. For these classes of algebras, centralisers and algebraic dependence are investigated. (c) 2007 Elsevier Inc. All rights reserved.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/646452
- author
- Hellstrom, Lars and Silvestrov, Sergei LU
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- commuting, generalised Weyl algebras, generalised Weyl structure, algebraic dependence, elements
- in
- Journal of Algebra
- volume
- 314
- issue
- 1
- pages
- 17 - 41
- publisher
- Elsevier
- external identifiers
-
- wos:000247710600002
- scopus:34249005317
- ISSN
- 0021-8693
- DOI
- 10.1016/j.jalgebra.2007.03.031
- language
- English
- LU publication?
- yes
- id
- 83f3fad5-feab-4eed-a633-0074d9d04d6b (old id 646452)
- date added to LUP
- 2016-04-01 11:47:11
- date last changed
- 2022-02-25 21:18:57
@article{83f3fad5-feab-4eed-a633-0074d9d04d6b, abstract = {{A property of algebraic dependence between two commuting elements is shown to hold in a more general setting than that in which it has previously been established. Key conditions are identified and some methods for establishing them are given. Moreover the class of algebras with a generalised Weyl structure, generalising the so-called Generalised Weyl Algebras (GWAs) or hyperbolic rings, is introduced and studied. We also present an interesting class of algebras which are not GWAs but share many of their properties by virtue of their generalised Weyl structure. For these classes of algebras, centralisers and algebraic dependence are investigated. (c) 2007 Elsevier Inc. All rights reserved.}}, author = {{Hellstrom, Lars and Silvestrov, Sergei}}, issn = {{0021-8693}}, keywords = {{commuting; generalised Weyl algebras; generalised Weyl structure; algebraic dependence; elements}}, language = {{eng}}, number = {{1}}, pages = {{17--41}}, publisher = {{Elsevier}}, series = {{Journal of Algebra}}, title = {{Ergodipotent maps and commutativity of elements in noncommutative rings and algebras with twisted intertwining}}, url = {{http://dx.doi.org/10.1016/j.jalgebra.2007.03.031}}, doi = {{10.1016/j.jalgebra.2007.03.031}}, volume = {{314}}, year = {{2007}}, }