The present work introduces the class of graded Lie-Rinehart algebras as a natural
generalization of graded Lie algebras. It is demonstrated that a tight G-graded Lie-Rinehart …

We study the structure of a graded $3 $-Lie-Rinehart algebra $\mathcal {L} $ over an
associative and commutative graded algebra $ A. $ For $ G $ an abelian group, we show …

Let g be a non-zero finite-dimensional split semisimple Lie algebra with root system Δ. Let Γ
be a finite set of integral weights of g containing Δ and {0}. We say that a Lie algebra L over …

For a given negatively graded Lie algebra K−, the universal graded Lie algebra U of type K−
is defined and its existence proved. By posing additional conditions on K−, other types of …

A ${\mathbb Z} _2\times {\mathbb Z} _2 $-graded Lie algebra $\mathfrak g $ is a ${\mathbb
Z} _2\times {\mathbb Z} _2 $-graded algebra $\mathfrak g $ with a bracket $[|.,.|] $ that …

The main objects of this thesis are graded Lie algebras associated with a Lie algebra or a
Lie algebroid such as the Frölicher-Nijenhuis algebra, the Kodaira-Spencer algebra and …

We study the structure of arbitrary graded Lie algebras. We show that any of such algebras L
with a symmetric G-support is of the form L= U+∑ j I j with U a subspace of L 1 and any I ja …

NOTTINGHAM LIE ALGEBRAS WITH DIAMONDS OF FINITE TYPE Page 1 February 3, 2004
10:35 WSPC/132-IJAC 00163 International Journal of Algebra and Computation Vol. 14, No. 1 …

We study the structure of graded Lie algebras of order 3 of arbitrary dimension and over an
arbitrary field ${\mathbb K} $. We show that any of such algebras $ L $ with a symmetric $ G …

One of the most considerable results of the theory of simple modular Lie algebras is the
proof of the generalized Kostrikin–Shafarevich hypothesis obtained by Strade and Wilson …