Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

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.

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inho...

In a paper by Xu, some simple Lie algebras of generalized Cartan type were constructed, using the mixtures of grading operators and down-grading operators. Among them, are the simple Lie algebras of generalized Witt type, which are in general nongraded and have no torus. In this paper, some representations of these simple Lie algebras of generalized Witt type are presented. 1. INTRODUCTION The ...

We derive the Green-Schwarz action on AdS 5 × S 5 using an alternate version of the coset superspace construction. By Wick rotations and Lie algebra identifications we bring the coset to GL(4|4)/(Sp(4) ⊗ GL(1)) 2 , which allows us to represent the conformal transformations on unconstrained matrices. The derivation is more streamlined even for the bosonic sector, and conformal symmetry is manife...

We review the matrix bases for a family of noncommutative ? products based on a Weyl map. These products include the Moyal product, as well as the Wick–Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity.

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane wave and a copropagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic for...

Let H be the corner-transfer-matrix Hamiltonian for the six-vertex model in the antiferroelectric regime. It acts on the infinite tensor product W = V ⊗ V ⊗ V ⊗ · · ·, where V is the 2-dimensional irreducible representation of the quantum affine Lie algebra Uq ( ŝl (2) ) . We observe that H is the derivation of Uq ( ŝl (2) ) , and conjecture that the eigenvectors of H form the level-1 vacuum re...

Definition 1.1. A Poisson algebra is an associative algebra A over a field K (fixed, of characteristic zero), equipped with a Lie bracket {−,−} such that {x,−} is a derivation for any x ∈ A, i.e. {x, yz} = {x, y}z + y{x, z}. Definition 1.2. A Poisson structure on a manifold M is a Poisson bracket {−,−} on the algebra C∞(M). Example 1.3. On T ∗Rn with position coordinates q1, ..., qn and momentu...