Journal of Algebra最新文献

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On the arithmetic of ultraproducts of commutative cancellative monoids

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.017

Daniel Windisch

We develop first steps in the study of factorizations of elements in ultraproducts of commutative cancellative monoids into irreducible elements. A complete characterization of the (multi-)sets of lengths in such objects is given. As applications, we show that several important properties from factorization theory cannot be expressed as first-order statements in the language of monoids, and we construct integral domains that realize every multiset of integers larger 1 as a multiset of lengths. Finally, we give a new proof (based on our ultraproduct techniques) of a theorem by Geroldinger, Schmid and Zhong from additive combinatorics and we propose a general method for applying ultraproducts in the setting of non-unique factorizations.

引用次数: 0

Distributive properties of division points and discriminants of Drinfeld modules

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.016

Ernst-Ulrich Gekeler

We present a new notion of distribution and derived distribution of rank

r \in N

for a global function field K with a distinguished place ∞. It allows to describe the relations between division points, isogenies, and discriminants both for a fixed Drinfeld module of rank r for the above data, or for the corresponding modular forms.

We introduce and study three basic distributions with values in

Q

, in the group

μ (\overline{K})

of roots of unity in the algebraic closure

\overline{K}

of K, and in the group

U^{(1)} (C_{\infty})

of 1-units of the completed algebraic closure

C_{\infty}

K_{\infty}

, respectively.

There result product formulas for division points and discriminants that encompass known results (e.g. analogues of Wallis' formula for

{(2 π ı)}^{2}

in the rank-1 case, of Jacobi's formula

Δ = {(2 π ı)}^{12} q \prod {(1 - q^{n})}^{24}

in the rank-2 case, and similar boundary expansions for

r > 2

) and several new ones: the definition of a canonical discriminant for the most general case of Drinfeld modules and the description of the sizes of division and discriminant forms.

In the now classical case where

(K, \infty) = (F_{q} (T), \infty)

and

r = 1

, 2 or 3, we give explicit values for the logarithms of such forms.

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引用次数: 0

A negative answer to Complement Question for presilting complexes

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.020

Yu-Zhe Liu , Yu Zhou

In this paper using a geometric model we show that there is a presilting complex over a finite dimensional algebra, which is not a direct summand of a silting complex.

引用次数: 0

Level 2 standard modules for A9(2) and partition conditions of Kanade-Russell

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.11.031

Kana Ito

We give Z-monomial generators for the vacuum spaces of certain level 2 standard modules of type

A_{odd}^{(2)}

with indices running over integer partitions. In particular, we give a Lie theoretic interpretation of the Rogers-Ramanujan type identities of type

A_{9}^{(2)}

, which were conjectured by Kanade-Russell, and proven by Bringmann et al. and Rosengren.

引用次数: 0

Vertex-primitive s-arc-transitive digraphs of symplectic groups

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.018

Lei Chen, Michael Giudici, Cheryl E. Praeger

A digraph is s-arc-transitive if its automorphism group is transitive on directed paths with s edges, that is, on s-arcs. Although infinite families of finite s-arc transitive digraphs of arbitrary valency were constructed by the third author in 1989, existence of a vertex-primitive 2-arc-transitive digraph was not known until an infinite family was constructed by the second author with Li and Xia in 2017. This led to a conjecture by the second author and Xia in 2018 that, for a finite vertex-primitive s-arc-transitive digraph, s is at most 2, together with their proof that it is sufficient to prove the conjecture for digraphs with an almost simple group of automorphisms. This paper confirms the conjecture for finite symplectic groups.

引用次数: 0

Dimensions of τ-tilting modules over path algebras and preprojective algebras of Dynkin type

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.022

Toshitaka Aoki , Yuya Mizuno

In this paper, we introduce a new generating function called d-polynomial for the dimensions of τ-tilting modules over a given finite dimensional algebra. Firstly, we study basic properties of d-polynomials and show that it can be realized as a certain sum of the f-polynomials of the simplicial complexes arising from τ-rigid pairs. Secondly, we give explicit formulas of d-polynomials for preprojective algebras and path algebras of Dynkin quivers by using a close relation with W-Eulerian polynomials and W-Narayana polynomials. Thirdly, we consider the ordinary and exponential generating functions defined from d-polynomials and give closed-form expressions in the case of preprojective algebras and path algebras of Dynkin type

A

引用次数: 0

String algebras over local rings: Admissibility and biseriality

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.12.019

Raphael Bennett-Tennenhaus

For a path algebra over a noetherian local ground ring, the notion of an admissible ideal was defined by Raggi-Cárdenas and Salmerón. We characterise the conditions for admissibility, and use them to study semiperfect module-finite algebras over local rings whose quotient by the radical is a product of copies of the residue field. We define string algebras over local ground rings and recover the notion introduced by Butler and Ringel when the ground ring is a field. We prove they are biserial in a sense of Kiričenko and Kostyukevich. We describe the syzygies of the uniserial summands of the radical. We give examples of Bäckström orders that are string algebras over discrete valuation rings.

引用次数: 0

Supersymmetric extension of universal enveloping vertex algebras

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2025-01-03 DOI: 10.1016/j.jalgebra.2024.11.034

Uhi Rinn Suh , Sangwon Yoon

In this paper, we study the construction of the supersymmetric extensions of vertex algebras. In particular, for

N = n \in Z_{+}

, we show that the universal enveloping

N = n

SUSY vertex algebra of an

N = n

SUSY Lie conformal algebra can be extended to an

N = n^{'} > n

SUSY vertex algebra. Additionally, we investigate various superconformal vectors which induce the same SUSY structure but distinct conformal weight decompositions of a vertex algebra.

引用次数: 0

Categorical generic fiber

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2024-12-31 DOI: 10.1016/j.jalgebra.2024.12.013

Hayato Morimura

For flat proper families of algebraic varieties with a smooth fiber, we describe the abelian category of coherent sheaves on the generic fiber as a Serre quotient. As an application, we prove specialization of derived equivalence. As another application, we provide new examples of Fourier–Mukai partners via deformations.

引用次数: 0

A monoidal category viewpoint for translation functors for finite W-algebras

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra

Pub Date : 2024-12-27 DOI: 10.1016/j.jalgebra.2024.12.012

Elisabetta Masut

We re-interpret Goodwin's translation functors for a finite W-algebra

H_{ℓ}

as an action of a monoidal subcategory of

U (g)

-mod on the category of finitely generated

H_{ℓ}

-modules. This action is obtained by transporting the tensor product of

U (g)

-modules through Skryabin's equivalence. We apply this interpretation to show that the Skryabin equivalence by stages introduced by Genra and Juillard is an equivalence of

U (g)

-module categories.

引用次数: 0

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