Commutant Algebras in Representations of Lie Algebras of Vector Fields
نویسنده
چکیده
In this paper, we give an explicit description of the commutant algebras for vector fields Lie algebras Wn in their representations on Wm×n, m 6 n, which arises from the tensor product Nm CoindF n, for the basis field F of characteristic 0. The result is some analogue of Weyl’s classical reciprocity.
منابع مشابه
Universal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کاملArithmetic Deformation Theory of Lie Algebras
This paper is devoted to deformation theory of graded Lie algebras over Z or Zl with finite dimensional graded pieces. Such deformation problems naturally appear in number theory. In the first part of the paper, we use Schlessinger criteria for functors on Artinian local rings in order to obtain universal deformation rings for deformations of graded Lie algebras and their graded representations...
متن کاملClassification of Lie Subalgebras up to an Inner Automorphism
In this paper, a useful classification of all Lie subalgebras of a given Lie algebraup to an inner automorphism is presented. This method can be regarded as animportant connection between differential geometry and algebra and has many applications in different fields of mathematics. After main results, we have applied this procedure for classifying the Lie subalgebras of some examples of Lie al...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملEssays on representations of real groups Introduction to Lie algebras
This essay is intended to be a self-contained if rather brief introduction to Lie algebras. The first several sections deal with Lie algebras as spaces of invariant vector fields on a Lie group. The very first sections are concerned with different ways to consider vector fields. This early treatment is intended, among other things, to motivate the eventual introduction of abstract Lie algebras,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003