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Ergodipotent maps and commutativity of elements in noncommutative rings and algebras with twisted intertwining

Hellstrom, Lars and Silvestrov, Sergei LU (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.
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author
organization
publishing date
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
2007-12-11 09:38:19
date last changed
2017-02-26 03:27:45
@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},
  keyword      = {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},
  volume       = {314},
  year         = {2007},
}