8 problems

Let $\mathbf R$ be an invertible Yang–Baxter $R$-matrix satisfying … where $\lambda_i\ne\lambda_j$ if $i\ne j$. For each eigenvalue $\lambda_k$, let $\mathbf P_k$ denote the corres…

The paper develops a functorial approach to differential calculus over a commutative base ring, using functors from a category of topological algebras to sets and natural transform…

Let $\mathfrak{g}_0$ be a finite-dimensional Lie algebra and let $\mathfrak{g}=\mathfrak{g}_0\oplus\mathfrak{g}_1$ be a Lie superalgebra defined by Eq. (2.1). Let $U(\mathfrak{g})$…

Let $\mathfrak{g}_0$ be a finite-dimensional Lie algebra and let $\mathfrak{g}=\mathfrak{g}_0\oplus\mathfrak{g}_1$ be a Lie superalgebra defined by Eq. (2.1). Let…

Fullness conjecture. It should be possible to obtain fullness by a purely covariant approach, combining the advantages of sophisticated topoi with those of a simple approach.

Let $U$ be the domain of a map $f$, let $p\in U$, and for each relevant order $j$ let $f^{\rangle j\langle}(\mathbf v;\mathbf s)$ denote the corresponding generalized divided diffe…

Let $k$ be a nonnegative integer, and let $\mathcal C^{[k]}$ and $\mathcal C^{\langle k\rangle}$ denote the two classes of maps defined in the paper using cubic and generalized div…

Let $\mathbb{K}$ be a field, and consider the notions of simplicial smoothness and cubical smoothness for maps defined using simplicial and cubic divided differences, respectively.…