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On centerless commutative automorphic loops

Gábor P. Nagy (2014)

Commentationes Mathematicae Universitatis Carolinae

In this short paper, we survey the results on commutative automorphic loops and give a new construction method. Using this method, we present new classes of commutative automorphic loops of exponent 2 with trivial center.

On dimension of the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand (2011)

Open Mathematics

Let L be an n-dimensional non-abelian nilpotent Lie algebra and s ( L ) = 1 2 ( n - 1 ) ( n - 2 ) + 1 - dim M ( L ) where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.

On the classification of 3 -dimensional F -manifold algebras

Zhiqi Chen, Jifu Li, Ming Ding (2022)

Czechoslovak Mathematical Journal

F -manifold algebras are focused on the algebraic properties of the tangent sheaf of F -manifolds. The local classification of 3-dimensional F -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional F -manifold algebras over the complex field .

On the definition of the dual Lie coalgebra of a Lie algebra.

Bertin Diarra (1995)

Publicacions Matemàtiques

Let L be a Lie algebra over a field K. The dual Lie coalgebra Lº of L has been defined by W. Michaelis to be the sum of all good subspaces V of the dual space L* of L: V is good if tm(V) ⊂ V ⊗ V, where m is the multiplication of L. We show that Lº = tm-1(L* ⊗ L*) as in the associative case.

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