5 papers
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…
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…
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…
Enveloping algebras of derivations of commutative and noncommutative algebras
Jason Bell, Lucas Buzaglo
Let 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…
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 and its modules have become increasingly prominent in both physics and mathematics i…