Generalized derivations on algebras
(2002) In LUTFMA-5019-2002/1-92/(2002)- 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:
http://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- unpublished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
- LUTFMA-5019-2002/1-92/(2002)
- issue
- 18
- pages
- 92 pages
- 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
- 2016-04-16 07:05:25
@misc{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}, series = {LUTFMA-5019-2002/1-92/(2002)}, title = {Generalized derivations on algebras}, year = {2002}, }