Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

Abstract

Let g be an affine Kac-Moody algebra, and µ a diagram automorphism of g. In this paper, we give an explicit realization for the universal central extension g[µ] of the twisted loop algebra of g related to µ, which provides a Moody-Rao-Yokonuma presentation for the algebra g[µ] when µ is nontransitive, and the presentation is indeed related to the quantization of toroidal Lie algebras. √ −1/N . In this paper, we study the universal central extension g[µ] of L(ḡ,μ), and give Moody-Rao-Yokonuma presentation for g [µ] when µ is non-transitive. One may expect that the MRY 2010 Mathematics Subject Classification. 17B67.

High density with elliptic flows

“…The consistency of nuclear-structure results for the low-density behavior of the symmetry energy appears to be increasing. The analysis of the dipole polarizability in 208 Pb performed by Zhang and Chen [49] and discussed at this conference [11,50] confirms the trend shown in Fig. 4 towards densities around ρ 0 /3.…”

“…where K sym is the still fairly unknown coefficient of the quadratic or curvature term [10,11]. The authors quote also error margins representative for the variation of the individual results as ∆E sym (ρ 0 ) = 2.7 MeV and ∆L = 16 MeV and conclude that L has a value about twice as large as E sym (ρ 0 ).…”

Drinfeld-type presentations of loop algebras

“…Let g[µ] be the subalgebra of g fixed by µ, which is the Lie algebra concerned about in this paper. It was known ( [K1,CJKT2]) that g [µ] is the universal central extension of the (twisted) loop algebra L(g, µ) = Span C {t m 1 ⊗ x (m) | x ∈ g, m ∈ Z} ⊂ L(g) (1.5) of g associated to µ, where x (m) = k∈Z N ξ −km µ k (x) and Z N = Z/NZ. The main goal of this paper is to provide a general construction of certain current type presentations for g [µ], which are loop analogues of the Serre-Gabber-Kac presentation for g.…”

“…The lemma is obviously when g is of finite type. For the affine case, this lemma was proved in [CJKT2,Lemma 3.2]. For convenience of the readers, we describe the explicit action of µ on g as follows:…”

“…We define g[µ] to be the subalgebra of g fixed by µ. It was known ( [K1,CJKT2]) that the restriction map (see (3.6))…”