Title of Dissertation: Motion Control for Nonholonomic Systems on Matrix Lie Groups Herbert Karl Struemper, Doctor of Philosophy, 1997 Dissertation directed by: Professor P. S. Krishnaprasad Department of Electrical Engineering In this dissertation we study the control of nonholonomic systems defined by invariant vector fields on matrix Lie groups. We make use of canonical constructions of coor...

We prove that the centralizer Cφ ⊆ HomR(M,M) of a nilpotent endomorphism φ of a finitely generated semisimple left R-module RM (over an arbitrary ring R) is the homomorphic image of the opposite of a certain Z(R)-subalgebra of the full m×m matrix algebra Mm×m(R[t]), where m is the dimension (composition length) of ker(φ). If R is a finite dimensional division ring over its central subfield Z(R)...

We present an original algebraic method for cycle enumeration which is well-suited for symbolic computations. Nilpotent adjacency matrix methods are employed to enumerate k-cycles in simple graphs on n vertices for any k ≤ n. Experimental results detailing computation times (in seconds) are compared with algorithms based on the approaches of Bax and Tarjan for perspective.

We describe a new algorithm for nding matrix representations for polycyclic groups given by nite presentations. In contrast to previous algorithms, our algorithm is e cient enough to construct representations for some interesting examples. The examples which we studied included a collection of free nilpotent groups, and our results here led us to a theoretical result concerning such groups.

This paper outlines a proof of the Jordan Normal Form Theorem. First we show that a complex, finite dimensional vector space can be decomposed into a direct sum of invariant subspaces. Then, using induction, we show the Jordan Normal Form is represented by several cyclic, nilpotent matrices each plus an eigenvalue times the identity matrix – these are the Jordan

Abstract Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg’s count of unipotent elements, Rudvalis and Shindoda’s work on the fixed space of a random matrix, and Lusztig’s work on counting nilpotent matrices of ...

We construct an explicit set of algebraically independent generators for the center of the universal enveloping algebra of the centralizer of a nilpotent matrix in the general linear Lie algebra over a field of characteristic zero. In particular, this gives a new proof of the freeness of the center, a result first proved by Panyushev, Premet and Yakimova.

Periodic tree are combinatorial structures which are in bijection with cluster tilting objects of affine type Ãn−1. The internal edges of the tree encode the c-vectors corresponding to the cluster tilting object. (See [8].) In this paper we assign a unipotent matrix to each tree, giving the relationship between cluster tilting objects and (pro)pictures for torsion-free (pro)nilpotent groups.