On The Lie Group of Umbrella Matrices

Authors : N. KURUOĞLU

Pages : 0-0

Doi:10.1501/Commua1_0000000231

View : 25 | Download : 7

Publication Date : 1983-01-01

Article Type : Research Paper

Abstract :In this paper, Umbrella matrices are defined which are selected from GL insert ignore into journalissuearticles values(n, |^ ); and it i» shown that Umbrella matrices form a matrix group with respect to the matrix product. Next, a characterization of Umbrella matrices is given; among these it İs proved that the gro­ up of Umbrella matices which are selected from O insert ignore into journalissuearticles values(n); and the group of Doubly Umbrella matrices are subgroup of Umbrella matrices which are selected from GL insert ignore into journalissuearticles values(n, Later it is shown that this matrix group is a Lie subgroup of GL insert ignore into journalissuearticles values(n, and a characteristic property is given about this Lie group. Finally it is shown that, the Lie group under consideration is not connected and noncompact are shown. At the end of this work, the Maurer-Cartan forms are investigated and using the prin- cipal I-forms the dimension of the Lie group under consideration is computed.
Keywords : Umbrella, characteristic, Maurer Cartan