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Generalized derivations on algebras

Harwig, Jonas and Silvestrov, Sergei LU (2002) In Preprints in Mathematical Sciences
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)
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author
and
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
twisted derivations, Jacobi identities, Witt algebra, Leibniz formulas
in
Preprints in Mathematical Sciences
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
2016-04-04 09:41:51
date last changed
2018-11-21 20:54:59
@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},
  language     = {eng},
  number       = {18},
  publisher    = {Lund University},
  series       = {Preprints in Mathematical Sciences},
  title        = {Generalized derivations on algebras},
  year         = {2002},
}