id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-1889	Barrett, Dennis I.; Biggs, Rory; Remsing, Claudiu C.	Affine Subspaces of the Lie Algebra se(1,1)	2014	16	.pdf	application/pdf	6423	359	83	REFERENCES 154 Appendix Table 1: Classification of affine subspaces and parametrized affine subspaces Type Affine subspaces Parametrized affine subspaces (1, 1) E1 + 〈E3〉   1 0 0 0 γ1 α   αE3 + 〈E1〉   0 1 0 0 α 0   (2, 0) 〈E1, E3〉   γ1 1 0 0 0 0 γ2 γ3 α     γ1 0 1 0 0 0 γ2 α 0   (2, 1) E2 + 〈E1, E3〉   γ1 1 0 β1 0 0 γ2 γ3 α     γ1 0 1 β1 0 0 γ2 α 0   E1 + 〈E1 + E2, E3〉   β1 1 0 0 1 0 γ1 γ2 β2     1 1 0 −1 1 0 γ1 γ2 β1     β1 0 1 0 0 1 γ1 β2 0     1 0 1 −1 0 1 γ1 β1 0   αE3 + 〈E1, E2〉   0 γ1 1 0 α 0 β1 0 0     0 β2 1 0 0 1 β1 0 0     0 1 1 0 −1 1 β1 0 0   α > 0, βi 6= 0, γi ∈ R REFERENCES 155 Table 2: Classification of parametrized (3,0)-affine subspaces Π : A+ u1B + u2C + u3D Classifying conditions Parametrized affine subspaces E∗3(〈C , D〉) 6= {0} E1 + E2, E1 − E2 /∈ We classify the full-rank affine subspaces (resp.	cache/ejpam-1889.pdf	txt/ejpam-1889.txt