For the inhomogeneous pseudo-unitary Lie algebras Iu(p, q) a determinantal method to compute the Casimir operators is given, independently of the traditional analysis of the enveloping algebra. This procedure is extended to contractions of Iu(p, q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p − 1, q), providing an alternative analytic...

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE, or, equivalently, the commutators of chiral fields. We discuss generalizations of vertex algebras and vertex Lie algebras, which are relevant for higher-dim...

In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30

Nonlinear generalization of the Dirac equation extending the standard paradigm of nonlinear Hamiltonians is discussed. “Faster-than-light telegraphs” are absent for all theories formulated within the new framework. A new metric for infinite dimensional Lie algebras associated with Lie-Poisson dynamics is introduced.

Let $\mathbb C_Q$ denote a rational quantum torus with $d$ variables, and $\mathcal Z$ be the centre of C_Q$. In this paper we give explicit description structure cuspidal modules for derivation Lie algebra D$ over C_Q$, an extra associative Z$-action.

A passive orthonomic system of PDEs defines a submanifold in the corresponding jet manifold, coordinated by so called parametric derivatives. We restrict the total differential operators and the prolongation of an evolutionary vector field v to this submanifold. We show that the vanishing of their commutators is equivalent to v being a generalized symmetry of the system. 1 Concerning the status...

We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra g. All n-point couplings with n ≥ 4 are completely determined in terms of the masses and the three-point couplings. A general fusing rule, formulated in the root space of the Lie algebra, is derived for all n-point couplings.