F[x,y] as a Dialgebra and a Leibniz Algebra |
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| Authors: | Lei Lin Yun Zhang |
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| Institution: | 1. Department of Mathematics , East China Normal University , Shanghai, China llin@math.ecnu.edu.cn;3. Department of Mathematics , East China Normal University , Shanghai, China |
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| Abstract: | In this article, we define a new associative dialgebra over a polynomial algebra Fx, y] with two indeterminates x and y. Left derivations, right derivations, derivations, and automorphisms of Fx, y] as associative dialgebra are determined. Meanwhile, we also determine all homogeneous derivations of Fx, y] as ?-graded Leibniz algebra, and automorphisms of Leibniz algebra Fx, y] preserving the standard filtration. |
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| Keywords: | Automorphism group Derivation algebra Dialgebra Leibniz algebra |
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