Central Extensions of Root Graded Lie Algebras
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
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arXiv subjects
Malihe Yousofzadeh
Publications and source records attributed to Malihe Yousofzadeh.
Extended affinization of Invariant Affine Reflection Algebras
Invariant affine reflection algebras are the last and the most general known extension of affine Kac-Moody Lie algebras, introduced in recent years. We develop a method known as "affinization" to the class of invariant affine reflection algebras, and show that starting with an algebra from this class together with a certain finite order automorphism, and applying the so called "loop construction", we obtain again an invariant affine reflection algebra. This can be considered as an important step towards the realization of invariant affine reflection algebras.
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Reflectable bases for affine reflection systems
The notion of a "root base" together with its geometry plays a crucial role in the theory of finite and affine Lie theory. However, it is known that such a notion does not exist for the recent generalizations of finite and affine root systems such as extended affine root systems and affine reflection systems. As an alternative, we introduce the notion of a "reflectable base", a minimal subset $Π$ of roots such that the non-isotropic part of the root system can be recovered by reflecting roots of $Π$ relative to the hyperplanes determined by $Π$. We give a full characterization of reflectable bases for tame irreducible affine reflection systems of reduced types, excluding types $E_{6,7,8}$. As a byproduct of our results, we show that if the root system under consideration is locally finite then any reflectable base is an integral base.
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Structure of root graded Lie algebras
We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.
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Locally finite admissible simple Lie algebras
We introduce a class of Lie algebras called admissible Lie algebras. We show that a locally finite admissible simple Lie algebra contains a nonzero maximal toral subalgebra and the corresponding root system is an irreducible locally finite root system.
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Exposition on affine and elliptic root systems and elliptic Lie algebras
This is an exposition in order to give an explicit way to understand (1) a non-topological proof for an existence of a base of an affine root system, (2) a Serre-type definition of an elliptic Lie algebra with rank =>2, and (3) the isotropic root multiplicities of those elliptic Lie algebras.
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Universal coverings of Lie tori (A finite presentation)
Using the well-known recognition and structural theorem(s) for root-graded Lie algebras and their universal coverings, we give a finite presentation for the universal covering algebra of a centerless Lie torus of type $X\not=A,C,BC$. We follow a unified approach for the types under consideration.
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A generalization of extended affine Lie algebrs
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and extended affine Lie algebras. Our results generalize well-known properties of these examples.
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Fixed Point Subalgebras of Extended Affine Lie Algebras
It is shown that the fixed point subalgebra of an EALA under a finite order automorphism (satisfying certain properties) is a sum of EALA's, an abelian subalgebra, and a subspace which is contained in the centralizer of the core.
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