Douglas, A. and Ali, A. (2026).
Wide regular subalgebras of Symmetrizable Kac-Moody algebras and an extension of Schur's lemma.
arXiv preprint arxiv.org/pdf/2606.01371, 14 pages.
Douglas, A. and de Graaf, W. A. (2025).
The subalgebras of the real forms of sl₃(C).
arXiv preprint arXiv:2502.00810, 39 pages.
Douglas, A., de Guise, H., and Repka, J. (2026).
Unitary and nonunitary representations of the Heisenberg–Weyl Lie algebra.
Journal of Physics A: Mathematical and Theoretical, 59(29), 295209.
Douglas, A. and Repka, J. (2025).
Narrow and wide regular subalgebras of semisimple Lie algebras.
Journal of Algebra 664, 348–361.
Douglas, A. and Repka, J. (2024).
Cyclic wide subalgebras of semisimple Lie algebras.
Communications in Algebra 53(4), 1321–1329.
Douglas, A. and de Graaf, W. A. (2021).
Closed subsets of root systems and regular subalgebras.
Journal of Algebra 565, 531–547.
Douglas, A., et al. (2018).
A comparison of two classifications of solvable Lie algebras.
Journal of Mathematical Physics 59(12), 121701, 18 pages.
Note: Co-authored with 11 undergraduate students at the University of Toronto, Canada.
Douglas, A. and Repka, J. (2018).
Subalgebras of the rank two semisimple Lie algebras.
Linear and Multilinear Algebra 66(10), 2049–2075.
Douglas, A. and Repka, J. (2017).
The subalgebras of the symplectic Lie algebra sp₄(C).
Linear Algebra and its Applications 527, 303–348.
Douglas, A. and Repka, J. (2016).
The subalgebras of so(4,C).
Communications in Algebra 44(12), 5269-5286.
Douglas, A. and Repka, J. (2016).
A classification of the subalgebras of A₂.
Journal of Pure and Applied Algebra 220(6), 2389-2413.
Douglas, A. and Repka, J. (2015).
Levi decomposable algebras in the classical Lie algebras.
Journal of Algebra 428, 292–314.
Douglas, A. and Repka, J. (2015).
The Levi decomposable subalgebras of C₂.
Journal of Mathematical Physics 56(5), 051703, 10 pages.
Douglas, A. and Repka, J. (2014).
The GraviGUT algebra is not a subalgebra of E₈, but E₈ does contain an Extended GraviGUT algebra.
SIGMA 10, 072, 10 pages.
Douglas, A., Repka, J., and Joseph, W. (2014).
The Euclidean algebra in rank 2 classical Lie algebras.
Journal of Mathematical Physics 55(6), 061701, 11 pages.
Douglas, A., de Guise, H., and Repka, J. (2013).
The Poincaré algebra in rank 3 simple Lie algebras.
Journal of Mathematical Physics 54(2), 023508, 12 pages.
Douglas, A., Kahrobaei, D., and Repka, J. (2013).
Classification of embeddings of abelian extensions of Dₙ into Eₙ₊₁.
Journal of Pure and Applied Algebra 217(10), 1942–1954.
Bremner, M. R. and Douglas, A. (2012).
The simple non-Lie Malcev algebra as a Lie–Yamaguti algebra.
Journal of Algebra 358, 269–291.
Douglas, A., Joseph, W., and Repka, J. (2011).
A classification of the embeddings of the Diamond Lie algebra into sl(4,C) and sp(4,C), and restrictions of irreducible modules.
Journal of Mathematical Physics 52(10), 103507, 11 pages.
Douglas, A. and Repka, J. (2011).
Embeddings of the Euclidean algebra e(3) into sl(4,C) and restriction of irreducible representations of sl(4,C).
Journal of Mathematical Physics 52(1), 013504, 12 pages.
Douglas, A. and Repka, J. (2011).
Indecomposable representations of the Euclidean algebra e(3) from irreducible representations of sl(4,C).
Bulletin of the Australian Mathematical Society 83(3), 439–449.
Douglas, A. and Repka, J. (2011).
Indecomposable representations of the Euclidean algebra e(3) from irreducible representations of the symplectic algebra sp(4, C).
Journal of Physics: Conference Series 284(1), 012022, 9 pages.
Douglas, A. and de Guise, H. (2010).
Some nonunitary, indecomposable representations of the Euclidean algebra.
Journal of Physics A: Mathematical and Theoretical 43.
Kahrobaei, D., Douglas, A., and Bencsath, K. (2010).
Some residually solvable one-relator groups.
Bulletin of the Irish Mathematical Society 65, 23–31.
Douglas, A. (2006).
On the finite dimensional, indecomposable representations of the Euclidean algebra e(2) having two generators.
Journal of Mathematical Physics 47(5).
Douglas, A. and Premat, A. (2007).
A class of nonunitary, finite dimensional representations of the Euclidean algebra e(2).
Communications in Algebra 35(5), 1433–1448.