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The partial compactification of the universal centralizer
The universal centralizer of a semisimple algebraic group G is the family of centralizers of regular elements, parametrized by their conjugacy...
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Additive maps related to Lie structure on factor von Neumann algebras
In this paper, we characterize additive Lie n-centralizers on factor von Neumann algebras at zero product as well as at projection product and show...
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Expansive Lie Group Actions
In this work, we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some...
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On Some Classes of Bases in Finite-Dimensional Lie Algebras
AbstractIn the paper, Lie algebras having bases of a special form (nice and beautiful bases) are considered. For nice bases, it is proved that, in...
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Lie Maps on Triangular Algebras Without Assuming Unity
We characterize Lie centralizer, Lie derivations and generalized Lie 2-derivations at zero products on triangular algebras without assuming unity....
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Characters for extended affine Lie algebras: a combinatorial approach
The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras....
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σ-Centralizers of Triangular Algebras
We present a characterization of the Lie (Jordan) σ -centralizers of triangular algebras. More precisely, it is proved that, under certain conditions,...
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ON THE MAXIMAL NILPOTENT ORBIT THAT INTERSECTS THE CENTRALIZER OF A MATRIX
We prove a simple algorithm, conjectured by Polona Oblak, for the determination of the maximal nilpotent orbit Q ( B ) that intersects the centralizer C B ...
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Real non-degenerate two-step nilpotent Lie algebras of dimension eight
We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex...
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On Maximal Extensions of Nilpotent Lie Algebras
AbstractExtensions of finite-dimensional nilpotent Lie algebras, in particular, solvable extensions, are considered. Some properties of maximal...
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Decomposition of Complete Color Hom-Lie Algebras
In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the...
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Lie groupoids and logarithmic connections
Using tools from the theory of Lie groupoids, we study the category of logarithmic flat connections on principal G -bundles, where G is a complex...
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Pre-Lie Algebras, Their Multiplicative Lattice, and Idempotent Endomorphisms
We introduce the notions of pre-morphism and pre-derivation for arbitrary non-associative algebras over a commutative ring k with identity. These...