7 citations · 30 across the 12 of their papers we have counts for
12 papers
Dynkin Diagrams and Short Peirce Gradings of Kantor Pairs
Bruce Allison, John Faulkner
In a recent article with Oleg Smirnov, we defined short Peirce (SP) graded Kantor pairs. For any such pair P, we defined a family, parameterized by the Weyl group of type BC_2, con…
Weyl images of Kantor pairs
Bruce Allison, John Faulkner, Oleg Smirnov
Kantor pairs arise naturally in the study of 5-graded Lie algebras. In this article, we begin the study of simple Kantor pairs of arbitrary dimension. We introduce Weyl images of K…
Some isomorphism invariants for Lie tori
Bruce Allison
In this paper we study the isomorphism problem for centreless Lie tori that are fgc (finitely generated as modules over their centroid). These Lie tori play a important role in the…
Multiloop algebras, iterated loop algebras and extended affine Lie algebras of nullity 2
Bruce Allison, Stephen Berman, Arturo Pianzola
Let M_n be the class of all multiloop algebras of finite dimensional simple Lie algebras relative to n-tuples of commuting finite order automorphisms. It is a classical result that…
Unitary Lie Algebras and Lie Tori of Type BC_r, r \geq 3
Bruce Allison, Georgia Benkart
A Lie G-torus of type X_r is a Lie algebra with two gradings -- one by an abelian group G and the other by the root lattice of a finite irreducible root system of type X_r. In this…
Multiloop realization of extended affine Lie algebras and Lie tori
Bruce Allison, Stephen Berman, John Faulkner +1
An important theorem in the theory of infinite dimensional Lie algebras states that any affine Kac-Moody algebra can be realized (that is to say constructed explicitly) using loop…