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Generalized derivations on algebras

Harwig, Jonas and Silvestrov, Sergei LU (2002) In Preprints in Mathematical Sciences1999-01-01+01:00
Abstract
In this paper we study (sigma,tau)-derivations on algebras from an abstract point of view. After some definitions and examples, we derive Leibniz type formulas and introduce a module structure on spaces of (sigma,tau)-derivations. Then we find all (sigma,tau)-derivations on unique factorization domains when sigma and tau are different endomorphisms. We also prove necessary equations for sigma-derivations on the quantum plane. Conditions for products and Jacobi type identities for (sigma,tau)-derivations on associative algebras are considered. Then follows an investigation of homogeneous (sigma,tau)-derivations on the Witt algebra of degree zero. Finally we generalize the Witt algebra to a skew-symmetric algebra of sigma-derivations on a... (More)
In this paper we study (sigma,tau)-derivations on algebras from an abstract point of view. After some definitions and examples, we derive Leibniz type formulas and introduce a module structure on spaces of (sigma,tau)-derivations. Then we find all (sigma,tau)-derivations on unique factorization domains when sigma and tau are different endomorphisms. We also prove necessary equations for sigma-derivations on the quantum plane. Conditions for products and Jacobi type identities for (sigma,tau)-derivations on associative algebras are considered. Then follows an investigation of homogeneous (sigma,tau)-derivations on the Witt algebra of degree zero. Finally we generalize the Witt algebra to a skew-symmetric algebra of sigma-derivations on a commutative associative algebra. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
twisted derivations, Jacobi identities, Witt algebra, Leibniz formulas
in
Preprints in Mathematical Sciences1999-01-01+01:00
issue
18
pages
92 pages
publisher
Lund University
external identifiers
  • Other:LUTFMA-5019-2002/1-92/(2002)
ISSN
1403-9338
project
Non-commutative Geometry in Mathematics and Physics
language
English
LU publication?
yes
id
4ca77267-6b9f-4602-8482-abf75503ed09 (old id 957649)
date added to LUP
2008-01-28 10:47:41
date last changed
2016-11-28 15:47:07
@article{4ca77267-6b9f-4602-8482-abf75503ed09,
  abstract     = {In this paper we study (sigma,tau)-derivations on algebras from an abstract point of view. After some definitions and examples, we derive Leibniz type formulas and introduce a module structure on spaces of (sigma,tau)-derivations. Then we find all (sigma,tau)-derivations on unique factorization domains when sigma and tau are different endomorphisms. We also prove necessary equations for sigma-derivations on the quantum plane. Conditions for products and Jacobi type identities for (sigma,tau)-derivations on associative algebras are considered. Then follows an investigation of homogeneous (sigma,tau)-derivations on the Witt algebra of degree zero. Finally we generalize the Witt algebra to a skew-symmetric algebra of sigma-derivations on a commutative associative algebra.},
  author       = {Harwig, Jonas and Silvestrov, Sergei},
  issn         = {1403-9338},
  keyword      = {twisted derivations,Jacobi identities,Witt algebra,Leibniz formulas},
  language     = {eng},
  number       = {18},
  pages        = {92},
  publisher    = {Lund University},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Generalized derivations on algebras},
  year         = {2002},
}