Degree Type

Dissertation

Date of Award

1991

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Jonathan D. H. Smith

Abstract

A new class of algebras, the so-called comtrans algebras that have recently arisen from the solution of a problem in differential geometry (cf. (1)), is investigated. Simple comtrans algebras determined by Lie algebras and by pairs of matrices are characterized. The two classes separate, except for the vector triple product algebra. It is shown that the representation theory of a comtrans algebra E and the representation theory of an associative universal envoloping algebra \widetilde M[subscript] E of E are equivalent. It is also shown that the universal enveloping algebra of a comtrans algebra E over a field and the tensor algebra over (E \wedge E) \oplus (E \otimes E) \oplus (E \otimes E) are isomorphic;A comtrans algebra CT(E,[beta]) from a pair (E,[beta]) consisting of a unital module E over a commutative ring R with 1 and a bilinear form [beta]:E[superscript]2 → R is produced. A "transposed" comtrans algebra CT(E,[beta])[superscript][tau] is also given by the pair (E,[beta]). It is shown that, under mild restrictions on the underlying model E, the automorphism groups of the formed space (E,[beta]) and of the comtrans algebras CT(E,[beta]) and CT(E,[beta])[superscript][tau] coincide. Conditions for a comtrans algebra to be a "form algebra" are also given.

DOI

https://doi.org/10.31274/rtd-180813-12874

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Xiaorong Shen

Language

en

Proquest ID

AAI9202388

File Format

application/pdf

File Size

55 pages

Included in

Mathematics Commons

Share

COinS