3 citations · 4 across the 10 of their papers we have counts for
15 papers
JSIR: An Audio-Aligned, Multi-Task Dataset of Jazz Standard Recordings
Sihun Lee, Dasaem Jeong
Beat tracking, chord estimation, and structure analysis are staple tasks of music information retrieval. Their datasets are drawn largely from Western popular music, and jazz remai…
Wide Regular Subalgebras of Symmetrizable Kac-Moody Algebras and an Extension of Schur's Lemma
Andrew Douglas, Abid Ali
The behavior of representations under restriction is a central theme in Lie theory. We study wide regular subalgebras of symmetrizable Kac--Moody algebras, extending work of Dougla…
Unitary and Nonunitary Representations of the Heisenberg-Weyl Lie Algebra
Andrew Douglas, Hubert de Guise, Joe Repka
We examine unitary and nonunitary representations of the Heisenberg-Weyl Lie algebra , with particular emphasis on tensor products of unitary representations and o…
Cyclic wide subalgebras of semisimple Lie algebras
Andrew Douglas, Joe Repka
Let be a Levi decomposable Lie algebra, with Levi factor , and radical . A module of $\ltimes…
Narrow, wide, and -wide regular subalgebras of semisimple Lie algebras
Andrew Douglas, Joe Repka
A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. From a finer viewpoi…
Regular extreme semisimple Lie algebras
Andrew Douglas, Joe Repka
A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. A subalgebra is narr…
Closed subsets of root systems and regular subalgebras
Andrew Douglas, Willem A. de Graaf
We describe an algorithm for classifying the closed subsets of a root system, up to conjugation by the associated Weyl group. Such a classification of an irreducible root system is…
Subalgebras of the rank two semisimple Lie algebras
Andrew Douglas, Joe Repka
In this expository article, we describe the classification of the subalgebras of the rank 2 semisimple Lie algebras. Their semisimple subalgebras are well-known, and in a recent se…
The subalgebras of the rank two symplectic Lie algebra
Andrew Douglas, Joe Repka
The semisimple subalgebras of the rank symplectic Lie algebra are well-known, and we recently classified its Levi decomposable subalgebras. In thi…
The subalgebras of
Andrew Douglas, Joe Repka
A classification of the semisimple subalgebras of the Lie algebra of traceless matrices with complex entries, denoted , is well-known. We classify its nonsemisimpl…
The subalgebras of
Andrew Douglas, Joe Repka
We classify the solvable subalgebras, semisimple subalgebras, and Levi decomposable subalgebras of , up to inner automorphism. By Levi's Theorem, this…
Some Residually Solvable One-Relator Groups
Delaram Kahrobaei, Andrew F. Douglas, Katalin Bencsáth
This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification…
Classification of embeddings of abelian extensions of into
Andrew Douglas, Delaram Kahrobaei, Joe Repka
An abelian extension of the special orthogonal Lie algebra is a nonsemisimple Lie algebra $D_n \inplus V$, where is a finite-dimensional representation of , with the…
The GraviGUT Algebra Is not a Subalgebra of , but Does Contain an Extended GraviGUT Algebra
Andrew Douglas, Joe Repka
The (real) GraviGUT algebra is an extension of the algebra by a -dimensional Lie algebra, but there is some ambiguity in the literature about its defini…
The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra
Murray R. Bremner, Andrew Douglas
The simple 7-dimensional Malcev algebra is isomorphic to the irreducible -module V(6) with binary product defined by the $\…