Results 21 to 30 of about 347 (81)

Koszul homomorphisms and universal resolutions in local algebra

Forum of Mathematics, Sigma
We define a local homomorphism $(Q,k)\to (R,\ell )$ to be Koszul if its derived fiber $R\otimes ^{\mathsf {L}}_Q k$ is formal, and if $\operatorname {Tor}^{Q}(R,k)$ is Koszul in the classical sense.
Benjamin Briggs, James C. Cameron, Janina C. Letz, Josh Pollitz   +3 more
doaj   +1 more source

Holomorphic field theories and higher algebra

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.
Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
wiley   +1 more source

Rational normal curves in weighted projective space

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2816-2837, September 2025.
Abstract This article aims to extend classical homological results about the rational normal curves to analogues in weighted projective spaces. Results include determinantality and nonstandard versions of quadratic generation and the Koszul property.
Caitlin M. Davis, Aleksandra Sobieska
wiley   +1 more source

Double Copy From Tensor Products of Metric BV■‐Algebras

Fortschritte der Physik, Volume 73, Issue 1-2, February 2025.
Abstract Field theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV■‐algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV■‐algebra.
Leron Borsten, Branislav Jurčo, Hyungrok Kim, Tommaso Macrelli, Christian Saemann, Martin Wolf   +5 more
wiley   +1 more source

Chow rings of matroids as permutation representations

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincaré duality and the Hard Lefschetz theorem.
Robert Angarone, Anastasia Nathanson, Victor Reiner   +2 more
wiley   +1 more source

PBW Deformations of Smash Products Involving Hopf Algebra of Kac–Paljutkin Type

Journal of Mathematics, Volume 2025, Issue 1, 2025.
Let H2n2 be the Kac–Paljutkin–type Hopf algebra of dimension 2n2, A its graded Koszul Artin–Schelter regular H2n2‐module algebra of Dimension 2, A! the Koszul dual of A, and Acop the braided‐opposite algebra of A. This paper describes (0, 1)‐degree PBW deformations of the smash product A♯H2n2 and those of A!♯H2n2 under the condition that the Koszul ...
Yujie Gao, Shilin Yang, Naihuan Jing
wiley   +1 more source

On the Witt group of the punctured spectrum of a regular semilocal ring

Journal of the London Mathematical Society, Volume 110, Issue 6, December 2024.
Abstract Let R$R$ be a regular semilocal ring of dimension 4q+1⩾5$4q+1\geqslant 5$ which contains 12$\frac{1}{2}$, l⩾1$l\geqslant 1$ the number of maximal ideals of R$R$ which are assumed to be all of the same height, and U$U$ the punctured spectrum of R$R$, that is, SpecR$\operatorname{Spec}R$ without the maximal ideals. We show that the Witt ring W(U)
Stefan Gille, Ivan Panin
wiley   +1 more source

Valuative invariants for large classes of matroids

Journal of the London Mathematical Society, Volume 110, Issue 3, September 2024.
Abstract We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a stressed subset. This framework provides a new combinatorial characterization of the class of (elementary) split matroids.
Luis Ferroni, Benjamin Schröter
wiley   +1 more source

Closed 3‐forms in five dimensions and embedding problems

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
wiley   +1 more source

On Rees algebras of 2‐determinantal ideals

Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.
Abstract Let I$I$ be the ideal of minors of a 2×n$2 \times n$ matrix of linear forms with the expected codimension. In this paper, we prove that the Rees algebra of I$I$ and its special fiber ring are Cohen–Macaulay and Koszul; in particular, they are quadratic algebras.
Ritvik Ramkumar, Alessio Sammartano
wiley   +1 more source