Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something which can be called a descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different, commutative subalgebra of...

In this paper we consider Q the class of solvable Lie algebras L with the following property: if A is a subalgebra of L, then Φ(A) ⊆ Φ(L) (where Φ(L) denotes the Frattini subalgebra of L;that is Φ(L) is the intersection of all maximal subalgebras of L). The class Q is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal...

Let G be an associative monomial k-algebra. If G is assumed to be finitely presented, then either G contains a free subalgebra on two monomials or else G has polynomial growth. If instead G is assumed to have finite global dimension, then either G contains a free subalgebra or else G has a finite presentation and polynomial growth. Also, a graded Hopf algebra with generators in degree one and r...

Let g be a reductive Lie algebra over C. We say that a g-module M is a generalized Harish-Chandra module if, for some subalgebra k ⊂ g, M is locally k-finite and has finite k-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when k is a Cartan subalgebra. We ...

We study the fixed point subalgebra of a certain class of lattice vertex operator algebras by an automorphism of order 3, which is a lift of a fixed-point-free isometry of the underlying lattice. We classify the irreducible modules for the subalgebra. Moreover, the rationality and the C2-cofiniteness of the subalgebra are established. Our result contains the case of the vertex operator algebra ...