Results 21 to 30 of about 51 (50)

Module structure of Weyl algebras

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract The seminal paper (Stafford, J. Lond. Math. Soc. (2) 18 (1978), no. 3, 429–442) was a major step forward in our understanding of Weyl algebras. Beginning with Serre's Theorem on free summands of projective modules and Bass' Stable Range Theorem in commutative algebra, we attempt to trace the origins of this work and explain how it led to ...
Gwyn Bellamy
wiley   +1 more source

Hall's marriage theorem

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract In 1935, Philip Hall published what is often referred to as ‘Hall's marriage theorem’ in a short paper (P. Hall, J. Lond. Math. Soc. (1) 10 (1935), no. 1, 26–30.) This paper has been very influential. I state the theorem and outline Hall's proof, together with some equivalent (or stronger) earlier results, and proceed to discuss some the many ...
Peter J. Cameron
wiley   +1 more source

Structure theorems for braided Hopf algebras

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We develop versions of the Poincaré–Birkhoff–Witt and Cartier–Milnor–Moore theorems in the setting of braided Hopf algebras. To do so, we introduce new analogs of a Lie algebra in the setting of a braided monoidal category, using the notion of a braided operad.
Craig Westerland
wiley   +1 more source

Growth problems in diagram categories

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3454-3469, November 2025.
Abstract In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
Jonathan Gruber, Daniel Tubbenhauer
wiley   +1 more source

Equivariant Hilbert and Ehrhart series under translative group actions

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study representations of finite groups on Stanley–Reisner rings of simplicial complexes and on lattice points in lattice polytopes. The framework of translative group actions allows us to use the theory of proper colorings of simplicial complexes without requiring an explicit coloring to be given.
Alessio D'Alì, Emanuele Delucchi
wiley   +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

Geometric realizations of the s‐weak order and its lattice quotients

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract For an n$n$‐tuple s${\bm{s}}$ of nonnegative integers, the s${\bm{s}}$‐weak order is a lattice structure on s${\bm{s}}$‐trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the s${\bm{s}}$‐weak order in terms of combinatorial objects ...
Eva Philippe, Vincent Pilaud
wiley   +1 more source

Fundamental motifs and parity within the crystallographic point groups

Journal of Applied Crystallography, Volume 58, Issue 4, Page 1447-1454, August 2025.
The Hasse diagram of the 3D point‐group classes is built with six motifs that have a well defined parity that determines their structure. Of the seven crystal systems, three are built with odd motifs, three are built with even motifs and the last one, the monoclinics, is `ambidextrous' as they are built with both.This paper analyzes the Hasse diagram ...
Maureen M. Julian, Matthew Macauley
wiley   +1 more source

The birational geometry of GIT quotients

Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 1952-1967, July 2025.
Abstract Geometric invariant theory (GIT) produces quotients of algebraic varieties by reductive groups. If the variety is projective, this quotient depends on a choice of polarisation; by work of Dolgachev–Hu and Thaddeus, it is known that two quotients of the same variety using different polarisations are related by birational transformations.
Ruadhaí Dervan, Rémi Reboulet
wiley   +1 more source