Results 41 to 50 of about 751 (85)

$\mathbf {5 \times 5}$ -graded Lie algebras, cubic norm structures and quadrangular algebras

Forum of Mathematics, Sigma
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show the following: (1) If the extremal geometry contains lines, then the Lie algebra admits a $5 \times 5$ -grading that can be ...
Tom De Medts, Jeroen Meulewaeter
doaj   +1 more source

Classification of generalized Wallach spaces [PDF]

Geometriae Dedicata, 2016, Vol. 181, N 1, 193-212, 2014
In this paper, we present the classification of generalized Wallach spaces and discuss some related problems.
arxiv   +1 more source

Combinatorics of the double shuffle Lie algebra

, 2012
In this article we give two combinatorial properties of elements satisfying the stuffle relations; one showing that double shuffle elements are determined by less than the full set of stuffle relations, and the other a cyclic property of their ...
S. Carr, Leila Schneps
semanticscholar   +1 more source

The automorphism groups and derivation algebras of two-dimensional algebras

, 2018
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.Comment: A type-mistake in $A_{3,2}(\mathbf{c})$ case, page 4, and its consequences are are ...
Ahmed, H., Bekbaev, U., Rakhimov, I.
core   +1 more source

On the existence of ad-nilpotent elements

, 1977
A condition sufficient to guarantee the nilpotence of a derivation of a Lie algebra is given. It is used to obtain an elementary proof that a finite dimensional Lie algebra over an algebraically closed field of arbitrary characteristic necessarily ...
G. Benkart, I. Isaacs
semanticscholar   +1 more source

Continuity of Lie mappings of the skew elements of Banach algebras with involution

, 1998
Let A and B be centrally closed prime complex Banach algebras with linear involution. If A is semisimple, then any Lie derivation of the skew elements of A is continuous and any Lie isomorphism from the skew elements of B onto the skew elements of A is ...
M. I. Berenguer, A. Villena
semanticscholar   +1 more source

Infinite-Dimensional Lie Algebras of Generalized Block Type [PDF]

, 1999
This paper investigates a class of infinite-dimensional Lie algebras over a field of characteristic 0 which are called here Lie algebras of generalized Block type, and which generalize a class of Lie algebras originally defined by Richard Block.
Osborn, J. Marshall, Zhao, Kaiming
core   +1 more source

The derivation algebra and automorphism group of the twisted Schrödinger-Virasoro algebra [PDF]

arXiv, 2008
In this article, we determine the derivation algebra and the automorphism group of the twisted Schr\"{o}dinger-Virasoro algebra.
arxiv  

Existence of ad-nilpotent elements and simple Lie algebras with subalgebras of codimension one

, 1988
For a perfect field F of arbitrary characteristic, the following statements are proved to be equivalent: (1) Any Lie algebra over F contains an ad-nilpotent element. (2) There are no simple Lie algebras over F having only abelian subalgebras.
V. R. Varea
semanticscholar   +1 more source

The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras [PDF]

arXiv, 2013
The groups of automorphisms of the Witt $W_n$ and Virasoro Lie algebras are found.
arxiv