Journal of Pure and Applied Algebra最新文献

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Central H-spaces and banded types 中心h空间和带状类型

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-14 DOI: 10.1016/j.jpaa.2025.107963

Ulrik Buchholtz , J. Daniel Christensen , Jarl G. Taxerås Flaten , Egbert Rijke

We introduce and study central types, which are generalizations of Eilenberg–Mac Lane spaces. A type is central when it is equivalent to the component of the identity among its own self-equivalences. From centrality alone we construct an infinite delooping in terms of a tensor product of banded types, which are the appropriate notion of torsor for a central type. Our constructions are carried out in homotopy type theory, and therefore hold in any ∞-topos. Even when interpreted into the ∞-topos of spaces, our approach to constructing these deloopings is new.

Along the way, we further develop the theory of H-spaces in homotopy type theory, including their relation to evaluation fibrations and Whitehead products. These considerations let us, for example, rule out the existence of H-space structures on the 2n-sphere for

n > 0

. We also give a novel description of the moduli space of H-space structures on an H-space. Using this description, we generalize a formula of Arkowitz–Curjel and Copeland for counting the number of path components of this moduli space. As an application, we deduce that the moduli space of H-space structures on the 3-sphere is

Ω^{6} S^{3}

我们引入并研究了中心类型，它是Eilenberg-Mac Lane空间的推广。当一个类型在它自己的自我等价中等价于同一性的组成部分时，它就是中心的。仅从中心性出发，我们用带型张量积构造了一个无限展开，带型张量积是中心型扭量的适当概念。我们的构造是在同伦类型理论中进行的，因此在任何∞-拓扑上都成立。即使被解释为空间的∞拓扑，我们构建这些发展的方法也是新的。在此过程中，我们进一步发展了同伦型理论中的h空间理论，包括它们与评价颤振和Whitehead积的关系。这些考虑让我们，例如，在n>；0的情况下，排除2n球上h空间结构的存在。我们还给出了h空间上h空间结构的模空间的一种新的描述。利用这一描述，我们推广了Arkowitz-Curjel和Copeland计算该模空间路径分量的公式。作为应用，我们推导出3球上h空间结构的模空间为Ω6S3。

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引用次数: 0

Comparison of Frobenius algebra structures on Calabi–Yau toric hypersurfaces

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107973

Jeehoon Park , Philsang Yoo

We establish an isomorphism between two Frobenius algebra structures, termed CY and LG, on the primitive cohomology of a smooth Calabi–Yau hypersurface in a simplicial Gorenstein toric Fano variety. As an application of our comparison isomorphism, we observe the existence of a Frobenius manifold structure on a finite-dimensional subalgebra of the Jacobian algebra of a homogeneous polynomial which may exhibit a non-compact singularity locus.

引用次数: 0

Idoneal genera and K3 surfaces covering an Enriques surface

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107974

Simon Brandhorst , Serkan Sonel , Davide Cesare Veniani

We introduce the notion of idoneal genera, which are a generalization of Euler's idoneal numbers. We prove that there exist only a finite number of idoneal genera, and we provide an algorithm to enumerate all idoneal genera of rank at least 3. As an application, we classify transcendental lattices of K3 surfaces covering an Enriques surface.

引用次数: 0

Compact groups in which commutators have finite right Engel sinks

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107970

Evgeny Khukhro , Pavel Shumyatsky

A right Engel sink of an element g of a group G is a subset containing all sufficiently long commutators

[. . . [[g, x], x], \dots, x]

. We prove that if G is a compact group in which, for some k, every commutator

[. . . [g_{1}, g_{2}], \dots, g_{k}]

has a finite right Engel sink, then G has a locally nilpotent open subgroup. If in addition, for some positive integer m, every commutator

[. . . [g_{1}, g_{2}], \dots, g_{k}]

has a right Engel sink of cardinality at most m, then G has a locally nilpotent subgroup of finite index bounded in terms of m only.

引用次数: 0

Finite groups with few character values that are not character degrees

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107969

Sesuai Y. Madanha , Xavier Mbaale , Tendai M. Mudziiri Shumba

<div><div>Let G be a finite group and <math><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math>. Define <math><mrow><mi>cv</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>χ</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>|</mo><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo><mi>g</mi><mo>∈</mo><mi>G</mi><mo>}</mo></math>, <math><mrow><mi>cv</mi></mrow><mo>(</mo><mi>χ</mi><mo>)</mo><mo>=</mo><mo>{</mo><mi>χ</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>|</mo><mi>g</mi><mo>∈</mo><mi>G</mi><mo>}</mo></math> and denote by <math><mrow><mi>dl</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math> the derived length of G. In the 1990s Berkovich, Chillag and Zhmud described groups G in which <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>χ</mi><mo>)</mo><mo>|</mo><mo>=</mo><mn>3</mn></math> for every non-linear <math><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math> and their results show that G is solvable. They also considered groups in which <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>χ</mi><mo>)</mo><mo>|</mo><mo>=</mo><mn>4</mn></math> for some non-linear <math><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math>. Continuing with their work, in this article, we prove that if <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>χ</mi><mo>)</mo><mo>|</mo><mo>⩽</mo><mn>4</mn></math> for every non-linear <math><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math>, then G is solvable. We also considered groups G such that <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>∖</mo><mrow><mi>cd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>=</mo><mn>2</mn></math>. T. Sakurai classified these groups in the case when <math><mo>|</mo><mrow><mi>cd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>=</mo><mn>2</mn></math>. We show that G is solvable and we classify groups G when <math><mo>|</mo><mrow><mi>cd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>⩽</mo><mn>4</mn></math> or <math><mrow><mi>dl</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>⩽</mo><mn>3</mn></math>. It is interesting to note that these groups are such that <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>χ</mi><mo>)</mo><mo>|</mo><mo>⩽</mo><mn>4</mn></math> for all <math><mi>χ</mi><mo>∈</mo><mrow><mi>Irr</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math>. Lastly, we consider finite groups G with <math><mo>|</mo><mrow><mi>cv</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>∖</mo><mrow><mi>cd</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>=</mo><mn>3</mn></math>. For nilpotent groups

引用次数: 0

Computation of the classifying ring of formal modules

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-11 DOI: 10.1016/j.jpaa.2025.107975

A. Salch

In this paper, we develop general machinery for computing the classifying ring

L^{A}

of one-dimensional formal A-modules, for various commutative rings A. We then apply the machinery to obtain calculations of

L^{A}

for various number rings and cyclic group rings A. This includes the first full calculations of the ring

L^{A}

in cases in which it fails to be a polynomial algebra. We also derive consequences for the solvability of some lifting and extension problems.

引用次数: 0

Groups with BCℓ-commutator relations

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107966

Egor Voronetsky

Isotropic odd unitary groups generalize Chevalley groups of classical types over commutative rings and their twisted forms. Such groups have root subgroups parameterized by a root system

{BC}_{ℓ}

and may be constructed by so-called odd form rings with Peirce decompositions. We show the converse: if a group G has root subgroups indexed by roots of

{BC}_{ℓ}

and satisfying natural conditions, then there is a homomorphism

inducing isomorphisms on the root subgroups, where

is the odd unitary Steinberg group constructed by an odd form ring

(R, Δ)

with a Peirce decomposition. For groups with root subgroups indexed by

A_{ℓ}

(the already known case) the resulting odd form ring is essentially a generalized matrix ring.

引用次数: 0

The third homology of projective special linear group of degree two

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107965

Behrooz Mirzaii , Elvis Torres Pérez

In this paper we investigate the third homology of the projective special linear group

{PSL}_{2} (A)

. As a result of our investigation we prove a projective refined Bloch-Wigner exact sequence over certain class of rings. The projective Bloch-Wigner exact sequence over an algebraically closed field of characteristic zero is a classical result and has many applications in algebra, number theory and geometry.

引用次数: 0

Hilbert scheme of a pair of skew lines on cubic threefolds 三次曲面上一对斜线的希尔伯特格式

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107971

Yilong Zhang

Two general lines on a smooth cubic threefold X are disjoint and determine an irreducible component of the Hilbert scheme of X. We prove that this component is smooth and isomorphic to the Hilbert scheme of two points of the Fano varieties of lines of X. We also study its relation to the geometry of lines and singularities on the hyperplane sections of X and its relation to Bridgeland moduli spaces.

在光滑三次立方X上的两条一般线是不相交的，并确定了X的Hilbert格式的一个不可约分量。我们证明了这个分量是光滑的，并且与X的Fano变直线的两点的Hilbert格式是同构的。我们还研究了它与X的超平面截面上的直线几何和奇点的关系，以及它与Bridgeland模空间的关系。

引用次数: 0

Infinitely many non-conjugate braid representatives of links 连杆的无穷多个非共轭辫状表示

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra

Pub Date : 2025-04-10 DOI: 10.1016/j.jpaa.2025.107964

Reiko Shinjo , Alexander Stoimenow

We prove that under a fairly general condition (that the edge strands are not fixed by the braid permutation) an iterated exchange move gives infinitely many non-conjugate braid representatives of links. More precisely, almost all braids obtained by iterated positive exchange moves are pairwise non-conjugate. As a consequence, every link with no trivial components has infinitely many conjugacy classes of n-braid representatives if and only if it has one admitting an exchange move.

我们证明了在一个相当一般的条件下（边链不被辫状排列固定），迭代交换给出了无穷多个链的非共轭辫状表示。更准确地说，几乎所有通过迭代的正交换动作得到的辫状结构都是非共轭的。因此，当且仅当它有一个允许交换移动的共轭类时，每个没有平凡分量的连杆都有无限多个n-辫表示的共轭类。

引用次数: 0

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