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A cohomological proof of Peterson-Kac's theorem of conjugacy of Cartan subalgebras of affine Kac-Moody Lie algebras
(Elsevier, 2014-02)
This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted ...
Finite-Dimensional Representations of Hyper Loop Algebras over Non-algebraically Closed Fields
(SpringerDordrechtHolanda, 2010)
Induced Modules for Affine Lie Algebras
(NATL ACAD SCI UKRAINE, INST MATH, 2009)
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra P of an affine Lie algebra G, our main result establishes the equivalence ...
Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
(European Mathematical Society, 2014-01)
Let M(n) be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that M(n) the class of all derived algebras ...
On conjugacy of Cartan subalgebras in extended affine Lie algebras
(Academic Press Inc Elsevier Science, 2016-02)
That finite-dimensional simple Lie algebras over the complex numbers can be classified by means of purely combinatorial and geometric objects such as Coxeter-Dynkin diagrams and indecomposable irreducible root systems, is ...
Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)
(ELSEVIER SCIENCE BV, 2009)
In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an ...
Conjugacy theorems for loop reductive group schemes and Lie algebras
(Springer, 2014-01)
The conjugacy of split Cartan subalgebras in the finite-dimensional simple case (Chevalley) and in the symmetrizable Kac–Moody case (Peterson–Kac) are fundamental results of the theory of Lie algebras. Among the Kac–Moody ...