MATHEMATICS research projects Observable subgroups of pro-affine algebraic groups We define a closed subgroup H of a pro-affine algebraic group G to be observable if every (finite-dimensional) rational H-module is an H sub-module of a rational G-module. We investigate the equivalence to observability of a number of other conditions on the pair (G, H) as in the case affine algebraic groups. Nahlus, N. In progress at AUB (sabbatical leave at University of California, Berkeley) Lie algebras of pro-affine algebraic groups We extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed field K of characteristic 0. Nahlus, N. In progress at AUB (sabbatical leave at University of California, Berkeley) Note on observable subgroups of linear algebraic groups Let H be an algebraic subgroup of a linear algebraic group G over an algebraically closed field K. If H contains a normal algebraic subgroup A which is observable in G such that H/A has non non-trivial rational characters, then H is observable in G. Nahlus, N. In progress at AUB (sabbatical leave at University of California, Berkeley) On extensions of representations of solvable Lie
algebras of arbitrary dimension Let A be a subLie algebra of a solvable Lie algebra L over an algebraically closed field of characteristic 0. We are interested in the problem of extending a finite-dimensional representation of A to a finite-dimensional representation of L. Nahlus, N. In progress at AUB (sabbatical leave at University of California, Berkeley) publication record Nahlus, N. 1997. Basic groups of Lie algebras and Hopf algebras. Pacific Journal of Mathematics 180: 135-151. Abstracts, Conferences, and Proceedings Nahlus, N. 1997. Note on faithful representations and a local property of Lie groups. Proceedings of the American Mathematical Society 125: 2767-2769. Nasri, A. March 1999. An algorithm for interpolating
intersecting curves by recursive subdivision surfaces. Shape Modeling
International '99, Aizu-Wakamatsu, Japan. Graduate Theses and Projects Abdul Baki, S. June 1999. The structure of rings with certain
conditions on elements. H. Abu-Khuzam. |