| Title | Generalized derivations on algebras |
| Authors | Jonas Harwig, Sergei Silvestrov |
| Publication | LUTFMA-5019-2002/1-92/(2002) |
| Year | 2002 |
| Issue | 18 |
| Pages | 92 |
| Document type | Preprint |
| Status | Published |
| Language | eng |
| Abstract English | 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. |
| Keywords | twisted derivations, Jacobi identities, Witt algebra, Leibniz formulas, |
| ISBN/ISSN/Other | ISSN: 1403-9338 |
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