WREATH PRODUCTS OF LIE ALGEBRAS.

Title: WREATH PRODUCTS OF LIE ALGEBRAS.
Identifier: AAI8023736
identifier: 8023736
Creator: SULLIVAN, FRANCES EVELLA.
Contributor: Gilbert Baumslag
Date: 1980
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In 1964 A. I. Smel'kin (Dokl. Akad, Nauk, SSSR 157 (1964) p. 149-170) introduced the notion of a verbal wreath product of groups. In 1973 Smel'kin (Trans. Moscow Math. Soc. 29 (1973) p. 239-252) introduced the analogous product for Lie algebras. However, in the spirit of group theory, we define wreath products in terms of generators and defining relations. This thesis may be viewed as an attempt to carry over to Lie algebras some theorems in group theory. Theorem 1. If A (NOT=) O is an abelian Lie algebra and T (NOT=) O is an arbitrary Lie algebra then the center of A wreath T is trivial. Theorem 2. If A (NOT=) O is an abelian Lie algebra and T (NOT=) O is an arbitrary Lie algebra when the wreath product of A and T is directly indecomposable. Theorem 3. Non-trivial free products of Lie algebras are (non-trivally) directly indecomposable. Theorem 4. Non-trivial free products of Lie algebras are not decomposable into non-trivial wreath products.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics