Application of abelian holonomy formalism to the elementary theory of numbers J. Math. Phys. 53, 052303 (2012) Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight J. Math. Phys. 53, 043510 (2012) Construction of time-dependent dynamical invariants: A new approach J. Math. Phys. 53, 042104 (2012) Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes Abstract. The aim of this paper is to complete the classification of three-dimensional complex Leibniz algebras. The description of isomorphism classes of three-dimensional complex Leibniz algebras has been given by Ayupov and Omirov in 1999. However, we found that this list has a little redundancy. In this paper we apply a method which is more elegant and it gives the precise list of isomorphism classes of these algebras. We compare our list with that of Ayupov-Omirov and show the corrections which should be made.
The present work is devoted to the extension of some general properties of automorphisms and derivations which are known for Lie algebras to finite dimensional complex Leibniz algebras. The analogues of the Jordan-Chevalley decomposition for derivations and the multiplicative decomposition for automorphisms of finite dimensional complex Leibniz algebras are obtained.2010 Mathematics Subject Classification. 17A32, 17A36, 17B40.
In this paper we describe the isomorphism classes of finitedimensional complex Leibniz algebras whose quotient algebra with respect to the ideal generated by squares is isomorphic to the direct sum of three-dimensional simple Lie algebra sl 2 and a threedimensional solvable ideal. We choose a basis of the isomorphism classes' representatives and give explicit multiplication tables.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.