The parentage between Weyl pairs, generalized Pauli group and unitary group is investigated in detail. We start from an abstract definition of the Heisenberg-Weyl group on the field R and then switch to the discrete Heisenberg-Weyl group or generalized Pauli group on a finite ring Zd. The main characteristics of the latter group, an abstract group of order d noted Pd, are given (conjugacy class...

0

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

The aim of this paper is to explain the bialgebra structure of the positive part of the quantized universal enveloping algebra (Drinfeld-Jimbo quantum group) of type Anusing the Lie algebra theory concepts. Recently has been introduced a generalization of Lie algebras, the basic T -Lie algebras [1]. Using the T -Lie algebra concept some new (we think) quantum groups of type Ancan be constructed...

We classify connected Lie groups which are locally isomorphic to generalized Heisenberg groups. For a given generalized Heisenberg group N , there is a one-to-one correspondence between the set of isomorphism classes of connected Lie groups which are locally isomorphic to N and a union of certain quotients of noncompact Riemannian symmetric spaces.

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.