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In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are obtained using a commutative diagram. This diagram leads not only to these properties, but also to an inequality for the degrees of representations and to an extension of Dedekinds theorem.
In this paper we study properties of a homomorphism $rho$ from the universal enveloping algebra $U=U(mathfrak{gl}(n+1))$ to a tensor product of an algebra $mathcal D(n)$ of differential operators and $U(mathfrak{gl}(n))$. We find a formula for the im
The largest eigenvalue of a networks adjacency matrix and its associated principal eigenvector are key elements for determining the topological structure and the properties of dynamical processes mediated by it. We present a physically grounded expre
We introduce a generalization of the notion of a negligible morphism and study the associated tensor ideals and thick ideals. These ideals are defined by considering deformations of a given monoidal category $mathcal{C}$ over a local ring $R$. If the
We investigate the fundamental properties of quantum Borcherds-Bozec algebras and their representations. Among others, we prove that the quantum Borcherds-Bozec algebras have a triangular decomposition and the category of integrable representations is semi-simple.
Let $Gamma$ be a generic subgroup of the multiplicative group $mathbb{C}^*$ of nonzero complex numbers. We define a class of Lie algebras associated to $Gamma$, called twisted $Gamma$-Lie algebras, which is a natural generalization of the twisted aff