In this paper, we study the simple modules for the restricted Lie superalgebra gl(m|n). A condition for the simplicity of the induced modules is given, and an analogue of Kac-Weisfeiler theorem is proved. Mathematics Subject Classification (2000): 17B50; 17B10.

Bloch and Okounkov’s correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of ĝl ∞ modules of level one. Recent works have calculated these character functions for higher levels for ĝl ∞ and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type D of h...

The category of group-graded modules over an abelian group G is a monoidal category. For any bicharacter of G this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have n-ary multiplications between various graded components. They possess universal enveloping algeb...

We define Lie groups and Lie algebras and show how invariant vector fields on a Lie group form a Lie algebra. We prove that this correspondence respects natural maps and discuss conditions under which it is a bijection. Finally, we introduce the exponential map and use it to write the Lie group operation as a function on its Lie algebra.

Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [8]. This leads to a classification problem. For example, in [4], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...

Bei sl2C wurden Darstellungen mittels ihrer Zerlegung in Eigenräume bezüglich des diagonalisierbaren Generators H analysiert. Die korrekte Verallgemeinerung dieses Vorgehens, hier am Beispiel sl3C vorgeführt, erlaubt es, jede beliebige halbeinfache Lie-Algebra g zu analysieren. Um die Allgemeinheit der Konzepte zu unterstreichen, wird im folgenden häufig g statt sl3C geschrieben, explizite Rech...

Let R be a 2-torsion free ring and L a Lie ideal of R. An additive mapping F : R ! R is called a generalized derivation on R if there exists a derivation d : R to R such that F(xy) = F(x)y + xd(y) holds for all x y in R. In the present paper we describe the action of generalized derivations satisfying several conditions on Lie ideals of semiprime rings.

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...