A Finite Number of Defining Relations and a Uce Theorem of the Elliptic Lie Algebras and Superalgebras with Rank ≥ 2
نویسنده
چکیده
In this paper, we give a finite number of defining relations satisfied by a finite number of generators for the elliptic Lie algebras and superalgebras gR with rank ≥ 2. Here the R’s denote the reduced and non-reduced elliptic root systems with rank ≥ 2. We also show that if L is an extended affine Lie algebra (EALA) whose non-isotropic roots form the R, then there exists a natural homomorphism F : gR → L, which also give a universal central extension (UCE) surjective map from [gR, gR] to the core of L. (More precisely, we take a ḡR instead of the gR.)
منابع مشابه
Fiber bundles and Lie algebras of top spaces
In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.
متن کاملUniversal 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 کاملOn Defining Relations of the Affine Lie Superalgebras and Their Quantized Universal Enveloping Superalgebras
Introduction. In this paper, we give defining relations of the affine Lie superalgebras and defining relations of a super-version of the Drinfeld[D1]Jimbo[J] affine quantized enveloping algebras. As a result, we can exactly define the affine quantized universal enveloping superalgebras with generators and relations. Moreover we give a Drinfeld’s realization of Uh(ŝl(m|n)). For the Kac-Moody Lie...
متن کاملLocally finite basic classical simple Lie superalgebras
In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.
متن کاملOn generalized reduced representations of restricted Lie superalgebras in prime characteristic
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 ...
متن کامل