نتایج جستجو برای: semisimple algebras

تعداد نتایج: 45462  

2011
R. Ameri R. A. Borzooei

In this paper we introduce the concepts of hyper P -semisimple Ialgebra and Abelian hyper I-algebra and we state and prove some related results. The hyper p-semi simple I-algebras is a generalization of p-semisimple BCI-algebras and a subclass of hyper I-algebras. Specially we show that every Abelian hyper I-algebra is a hyper psemisimple I-algebra and a commutative canonical hypergroup. In fol...

2012
JINGCHENG DONG LI DAI Jingcheng Dong Li Dai

Let p, q be distinct prime numbers, and k an algebraically closed field of characteristic 0. Under certain restrictions on p, q, we discuss the structure of semisimple Hopf algebras of dimension pq. As an application, we obtain the structure theorems for semisimple Hopf algebras of dimension 9q over k. As a byproduct, we also prove that odd-dimensional semisimple Hopf algebras of dimension less...

2015
IVAN LOSEV

We start by introducing Kac-Moody algebras and completing the classification of finite dimensional semisimple Lie algebras. We then discuss the classification of finite dimensional representations of semisimple Lie algebras (and, more generally, integrable highest weight representations of Kac-Moody algebras). We finish by discussing the structure and representation theory of reductive algebrai...

2012
Liping Li

There are many structures (algebras, categories, etc) with natural gradings such that the degree 0 components are not semisimple. Particular examples include tensor algebras with non-semisimple degree 0 parts, extension algebras of standard modules of standardly stratified algebras. In this thesis we develop a generalized Koszul theory for graded algebras (categories) whose degree 0 parts may b...

2009
RUTWIG CAMPOAMOR-STURSBERG

For any semisimple subalgebra s′ of exceptional Lie algebras s satisfying the constraint rank(s′) = rank(s)−1 we analyze the branching rules for the adjoint representation, and determine the compatibility of the components with Heisenberg algebras. The analysis of these branching rules allows to classify the contractions of exceptional algebras onto semidirect products of semisimple and Heisenb...

2008
R. Campoamor-Stursberg

The problem of non-solvable contractions of Lie algebras is analyzed. By means of a stability theorem, the problem is shown to be deeply related to the embeddings among semisimple Lie algebras and the resulting branching rules for representations. With this procedure, we determine all deformations of indecomposable Lie algebras having a nontrivial Levi decomposition onto semisimple Lie algebras...

2003
Fujio Kubo

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of ...

2017
DUSTAN LEVENSTEIN D. LEVENSTEIN

Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...

پایان نامه :وزارت علوم، تحقیقات و فناوری - دانشگاه ارومیه - دانشکده علوم 1393

در این پایان نامه مرکز ساز جبرهای عملگری استاندارد وh^*- جبرهای نیم ساده را بیان می کنیم. فرض کنیم a یک *h-جبر نیم ساده و t: a -> a یک نگاشت جمعی باشد به طوری که به ازای هر x∈a و بعضی n ≥ 1 داشته باشیم. 2t(x n+1) = t(x)xn + xnt(x) در این صورت t یک مرکزساز چپ و راست است. این پایان نامه بر اساس مقاله ی زیر نوشته شده است: i. kosi-ulbl and j. vukman, on centralizers of standard operator algebras ...

1998
Pavel Etingof

The goal of this paper is to give a new method of constructing finite-dimensional semisimple triangular Hopf algebras, including minimal ones which are non-trivial (i.e. not group algebras). The paper shows that such Hopf algebras are quite abundant. It also discovers an unexpected connection of such Hopf algebras with bijective 1-cocycles on finite groups and set-theoretical solutions of the q...

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