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To describe the representation theory of the quantum Weyl algebra at an $l$th primitive root $gamma$ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation $yx-gamma xy=1$, assuming $yx eq xy$. In this note, we complete their result by finding and classifying, up to equivalence, all irreducible matrix solutions $(X, Y)$, where $X$ is singular.
Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differential which satisfy finiteness conditions analogous to those of finitar
We discuss some aspects of the representation theory of the deformed Virasoro algebra $virpq$. In particular, we give a proof of the formula for the Kac determinant and then determine the center of $virpq$ for $q$ a primitive N-th root of unity. We d
In this paper we describe some Leibniz algebras whose corresponding Lie algebra is four-dimensional Diamond Lie algebra $mathfrak{D}$ and the ideal generated by the squares of elements (further denoted by $I$) is a right $mathfrak{D}$-module. Using d
In the present paper we describe Leibniz algebras with three-dimensional Euclidean Lie algebra $mathfrak{e}(2)$ as its liezation. Moreover, it is assumed that the ideal generated by the squares of elements of an algebra (denoted by $I$) as a right $m
We give a proof of Lusztigs conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at $ell$-th root of unity, where $ell$ is an odd prime power satisfying certain reasonable conditions.