Related papers: Kac-Moody Quaternion Lie Algebra
We construct certain Steinberg groups associated to extended affine Lie algebras and their root systems. Then by the integration methods of Kac and Peterson for integrable Lie algebras, we associate a group to every tame extended affine Lie…
Various questions on Lie ideals of C*-algebras are investigated. They fall roughly under the following topics: relation of Lie ideals to closed two-sided ideals; Lie ideals spanned by special classes of elements such as commutators,…
A survey of the theory of Kac polynomials for quivers and for curves. In particular, we describe the representation-theoretic meaning of Kac polynomials in terms of Hall algebras, and the geometric meaning of Kac polynomials in relation to…
A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three time-like coordinates, we have been able to consistently recover a suitable formulation of…
We construct a canonical basis for quantum generalized Kac-Moody algebra via semisimple perverse sheaves on varieties of representations of quivers. We compare this basis with the one recently defined purely algebraically by Jeong, Kang and…
The family of quaternionic quasi-unitary (or quaternionic unitary Cayley--Klein algebras) is described in a unified setting. This family includes the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well as many…
A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of deformations with respect to one algebra together with a trivialization with respect to the other. Such deformations occur commonly in Algebraic…
This is a companion article to my papers on Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebras gl(m|n) (much revised!) and q(n). The goal is to develop the general theory of tilting modules for Lie superalgebras,…
In this thesis, we consider several aspects of over-extended and very-extended Kac-Moody algebras in relation with theories of gravity coupled to matter. In the first part, we focus on the occurrence of KM algebras in the cosmological…
We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie…
We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our…
The present paper contains a systematic study of the structure of metric Lie algebras, i.e., finite-dimensional real Lie algebras equipped with a non-degenerate invariant symmetric bilinear form. We show that any metric Lie algebra without…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…
A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a…
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown…
We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.
Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, and the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary…
The focus of this thesis is on (1) the role of Ka\v c-Moody (KM) algebras in string theory and the development of techniques for systematically building string theory models based on higher level ($K\geq 2$) KM algebras and (2) fractional…
We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root $\alpha_{+4}$, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no…