On a connection between nilpotent groups and Lie rings.
On centerless commutative automorphic loops
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 with trivial center.
On dimension of the Schur multiplier of nilpotent Lie algebras
Let L be an n-dimensional non-abelian nilpotent Lie algebra and 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 prime -graded Lie algebras of growth one.
On Some Generalizations of Lie Algebras
On the classification of -dimensional -manifold algebras
-manifold algebras are focused on the algebraic properties of the tangent sheaf of -manifolds. The local classification of 3-dimensional -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional -manifold algebras over the complex field .
On the constructions of Tits and Faulkner: an isomorphism theorem.
On the definition of the dual Lie coalgebra of a Lie algebra.
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.
On the spectral set of a solvable Lie algebra of operators.
On the Structure of Reduced ...-Ternary Algebras of Degree > 2.