Lucas Buzaglo

activity

20212026

collaborators

9 papers

math.RA2026

Dual reflection groups for three-dimensional Artin--Schelter regular algebras

Lucas Buzaglo, Daniel Rogalski

By definition, a dual reflection group is a finite group which grades an Artin--Schelter regular algebra $A$ such that the identity component $A_{e}$ is again regular. In this paper,…

math.RA2026

Lie subalgebras of vector fields on curves

Lucas Buzaglo, Colin Ingalls

We study the subalgebra structure of Krichever-Novikov algebras, which are Lie algebras of vector fields on smooth affine curves. Our main result is that every infinite-dimensional…

math.RA2026

Coactions of cocommutative Hopf algebras on skew polynomial rings

Lucas Buzaglo, Daniel Rogalski

We classify the cocommutative Hopf algebras which coact inner-faithfully on (one-parameter) skew polynomial rings $A_q(n) = \Bbbk \langle x_1,\dots,x_n \rangle/(x_j x_i - q x_i x_j…

math.RT2025

On the boundary Carrollian conformal algebra

Lucas Buzaglo, Xiao He, Tuan Anh Pham +3

We initiate the mathematical study of the boundary Carrollian conformal algebra (BCCA), an infinite-dimensional Lie algebra recently discovered in the context of Carrollian physics…

math.RA2024

Enveloping algebras of derivations of commutative and noncommutative algebras

Jason Bell, Lucas Buzaglo

Let $k$ be a field of characteristic zero. Motivated by the fundamental question of whether it is possible for the universal enveloping algebra of an infinite-dimensional Lie a…

math.RA2024

Central extensions, derivations, and automorphisms of semi-direct sums of the Witt algebra with its intermediate series modules

Lucas Buzaglo, Girish S. Vishwa

Lie algebras formed via semi-direct sums of the Witt algebra $Der (C [t, t^{- 1}])$ and its modules have become increasingly prominent in both physics and mathematics i…

math.RA2023

Maximal dimensional subalgebras of general Cartan type Lie algebras

Jason Bell, Lucas Buzaglo

Let $k$ be a field of characteristic zero and let $W_{n} = Der (k [x_{1}, \dots, x_{n}])$ be the $n^{th}$ general Cartan type Lie algebra. In this pap…

math.RA2023

Derivations, extensions, and rigidity of subalgebras of the Witt algebra

Lucas Buzaglo

Let $k$ be an algebraically closed field of characteristic 0. We study some cohomological properties of Lie subalgebras of the Witt algebra $W = \operatorname{Der}(\Bbbk[t,t^{-…

math.RA2021

Enveloping algebras of Krichever-Novikov algebras are not noetherian

Lucas Buzaglo

This work is part of the overarching question of whether it is possible for the universal enveloping algebra of an infinite-dimensional Lie algebra to be noetherian. The main resul…