We define, for each subset $S$ of the set $\mathcal{P}$ primes, an $S_n$-module $Lie_n^S$ with interesting properties. $Lie_n^\emptyset$ is well-known representation $Lie_n$ $S_n$ afforded by free Lie algebra, while $Lie_n^\mathcal{P}$ module $C\!onj_n$ conjugacy action on $n$-cycles. For arbitrary $Lie_n^{S}$ interpolates between representations and $C\!onj_n.$ consider symmetric exterior powe...

It is well known that anomaly cancellations for D16 Lie algebra are at the root of the first string revolution. For E8 Lie algebra, cancellation of anomalies is the principal fact leading to the existence of heterotic string. They are in fact nothing but the 6th order cohomologies of corresponding Lie algebras. Beyond 6th order, the calculations seem to require special care and it could be that...

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

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.

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.