The weights of simple modules in Category <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">O</mml:mi></mml:math> for Kac–Moody algebras

study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour

this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...

The category of generalized crossed modules

In the definition of a crossed module $(T,G,rho)$, the actions of the group $T$ and $G$ on themselves are given by conjugation. In this paper, we consider these actions to be arbitrary and thus generalize the concept of ordinary crossed module. Therefore, we get the category ${bf GCM}$, of all generalized crossed modules and generalized crossed module morphisms between them, and investigate som...

On Lie Algebras in the Category of Yetter - Drinfeld Modules

The category of Yetter-Drinfeld modules YD K over a Hopf algebra K (with bijektive antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in YD K such that the set of primitive elements P (H) is a Lie algebra in this sense...

Simple modules of Ariki{Koike algebras

Simple modules for the restricted Cartan type Lie algebras

The simple modules with homogeneous characters are considered, their dimension formulas are determined.