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 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:
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- unpublished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: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}}, keywords = {{twisted derivations; Jacobi identities; Witt algebra; Leibniz formulas}}, language = {{eng}}, number = {{18}}, publisher = {{Lund University}}, series = {{Preprints in Mathematical Sciences}}, title = {{Generalized derivations on algebras}}, year = {{2002}}, }