The class of locally compact groups admits a strong structure theory. This is due to the fact that—via approximation (projective limits)—important parts of the theory of Lie groups and Lie algebras carry over. This phenomenon becomes particularly striking if one assumes, in addition, that the groups under consideration are connected and of finite dimension. The aim of the present notes is to co...

We show that a set of monic polynomials in the free Lie superalgebra is a Gröbner-Shirshov basis for a Lie superalgebra if and only if it is a Gröbner-Shirshov basis for its universal enveloping algebra. We investigate the structure of GröbnerShirshov bases for Kac-Moody superalgebras and give explicit constructions of Gröbner-Shirshov bases for classical Lie superalgebras. Supported in part by...

Let Am,n be the tensor product of Laurent polynomial algebra in m even variables and exterior n odd over complex field C, Witt superalgebra Wm,n Lie superderivations Am,n. In this paper, we classify simple weight modules with finite-dimensional spaces respect to standard Cartan subalgebra Wm,0. Every such module is either a quotient or highest type.

Let $\mathfrak{d}$ be the Lie superalgebra of superderivations sheaf sections exterior algebra homogeneous vector bundle $E$ over flag variety $G/P$, where $G$ is a simple finite-dimensional complex group and $P$ its parabolic subgroup. Then, transitive irreducible whenever defined by an $P$-module $V$ such that highest weight $V^*$ dominant. Moreover, simple; it isomorphic to fields on superpo...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

In this paper complexes of generalized Verma modules over the infinitedimensional exceptional Lie superalgebras E(3, 8) and E(5, 10) are constructed and studied. 0. Introduction. In our papers [KR1]–[KR3] we constructed all degenerate irreducible modules over the exceptional Lie superalgebra E(3, 6). In the present paper we apply the same method to the exceptional Lie superalgebras E(3, 8) and ...

Abstract We introduce a new approach to the study of finite-dimensional representations quantum group affine Lie superalgebra $ \textrm {L}{\mathfrak {g}\mathfrak {l}}_{M|N}=\mathbb {C}[t,t^{-1}]\otimes \mathfrak {l}_{M|N}$ ($M\neq N$). explain how {l}}_{M|N}$ are directly related those algebra type $A$, using an exact monoidal functor called truncation. This can be viewed as analogue super dua...