Generalized derivations on algebras
(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 sigmaderivations 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 skewsymmetric algebra of sigmaderivations 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 sigmaderivations 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 skewsymmetric algebra of sigmaderivations on a commutative associative algebra. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/957649
 author
 Harwig, Jonas and Silvestrov, Sergei ^{LU}
 organization
 publishing date
 2002
 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 unpublished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:LUTFMA50192002/192/(2002)
 ISSN
 14039338
 project
 Noncommutative Geometry in Mathematics and Physics
 language
 English
 LU publication?
 yes
 id
 4ca772676b9f46028482abf75503ed09 (old id 957649)
 date added to LUP
 20160404 09:41:51
 date last changed
 20181121 20:54:59
@article{4ca772676b9f46028482abf75503ed09, 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 sigmaderivations 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 skewsymmetric algebra of sigmaderivations on a commutative associative algebra.}, author = {Harwig, Jonas and Silvestrov, Sergei}, issn = {14039338}, language = {eng}, number = {18}, publisher = {Lund University}, series = {Preprints in Mathematical Sciences}, title = {Generalized derivations on algebras}, year = {2002}, }