Related papers: On extensions and branching rules for modules clos…
Given a ring object $A$ in a symmetric monoidal category, we investigate what it means for the extension $\mathbb{1}\rightarrow A$ to be (quasi-)Galois. In particular, we define splitting ring extensions and examine how they occur.…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…
The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be…
We demonstrate a novel strong law of large numbers for branching processes, with a simple proof via measure-theoretic manipulations and spine theory. Roughly speaking, any sequence of events that eventually occurs almost surely for the…
We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of curves (conformal blocks) associated to modular fusion…
We consider the possibility of semisimple tensor categories whose fusion rule includes exactly one noninvertible simple object. Conditions are given for the existence or nonexistence of coherent associative structures for such fusion rules,…
We discuss recent developments on branching problems of irreducible unitary representations $\pi$ of real reductive groups when restricted to reductive subgroups. Highlighting the case where the underlying $(g,K)$-modules of $\pi$ are…
Let n be a positive integer and let Sigma_n be the symmetric group of degree n. Let S^lambda be the Specht module for Sigma_n corresponding to a partition lambda of n, defined over a field F of odd characteristic. We find the indecomposable…
There exist irreducible exact covering systems (ECS). These are ECS which are not a proper split of a coarser ECS. However, an ECS admiting a maximal modulus which is divisible by at most two distinct primes, primely splits a coarser ECS.…
We review a class of modules for the wreath product S(m) wr S(n) of two symmetric groups which are analogous to the Specht modules of the symmetric group, and prove a pair of branching rules for this family of modules. These branching rules…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
In this paper, we derive a Singleton bound for lattice schemes and obtain Singleton bounds known for binary codes and subspace codes as special cases. It is shown that the modular structure affects the strength of the Singleton bound. We…
We propose new structures called almost o-minimal structures and $\mathfrak X$-structures. The former is a first-order expansion of a dense linear order without endpoints such that the intersection of a definable set with a bounded open…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Complete hyperbolicity of small Euclidean balls with respect to a C^1-smooth almost complex structure standard at origin is improved to give a complete hyperbolicity of strictly pseudoconvex domains. More precise (and lower) regularity…
Categorical aspects of the theory of modules over trusses were studied in recent years. The snake lemma and the nine lemma in categories of modules over trusses are formulated in this paper.
We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all…
We define and study the notion of a crossed module over an inverse semigroup and the corresponding $4$-term exact sequences, called crossed module extensions. For a crossed module $A$ over an $F$-inverse monoid $T$, we show that equivalence…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…