In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra \(C^{(1)}_\ell\), \(\ell\geq2\), and similar with no obvious connection representation theory algebras.

A condition on an affine central subalgebra Z of a noetherian algebra A of finite GelfandKirillov dimension, which we call here unruffledness, is shown to be equivalent in some circumstances to the flatness of A as a Z-module. Unruffledness was studied by Borho and Joseph in work on enveloping algebras of complex semisimple Lie algebras, and we discuss applications of our result to enveloping a...

Introduction. In this paper, we give defining relations of the affine Lie superalgebras and defining relations of a super-version of the Drinfeld[D1]Jimbo[J] affine quantized enveloping algebras. As a result, we can exactly define the affine quantized universal enveloping superalgebras with generators and relations. Moreover we give a Drinfeld’s realization of Uh(ŝl(m|n)). For the Kac-Moody Lie...

assume that $(n,l)$, is a pair of finite dimensional nilpotent lie algebras, in which $l$ is non-abelian and $n$ is an ideal in $l$ and also $mathcal{m}(n,l)$ is the schur multiplier of the pair $(n,l)$. motivated by characterization of the pairs $(n,l)$ of finite dimensional nilpotent lie algebras by their schur multipliers (arabyani, et al. 2014) we prove some properties of a pair of nilpoten...