TY - JOUR
ID - 2079
TI - Exponential map and invariant form on generalized Lie groups
JO - Iranian Journal of Science and Technology (Sciences)
JA - IJSTS
LA - en
SN - 1028-6276
AU - Farhangdoost, M. R.
AD - Department of Mathematics, College of Sciences, Shiraz University, P. O. Box 71457-44776, Shiraz, Iran
Y1 - 2012
PY - 2012
VL - 36
IS - 3
SP - 293
EP - 298
KW - Lie group
KW - exponential map
KW - differential invariant form
DO - 10.22099/ijsts.2012.2079
N2 - In this paper, by definition of exponential map of the Lie groups the concept of exponential map of generalized Lie groups is introduced. This has a powerful generalization to generalized Lie groups which takes each line through the origin to an order product of some one-parameter subgroup. We show that the exponential map is a - map. Also, we prove some important properties of the exponential map for generalized Lie groups. Under the identification, it is shown that the derivative of the exponential map is the identity map. One of the most powerful applications of these exponential maps is to define generalized adjoint representation of a top space, so we show that this representation is a - map. Finally, invariant forms are introduced on a generalized Lie group. We provemthat every left invariant -form are introduced on a generalized Lie group with the finite number of identity elements is . At the end of this paper, for compact connected generalized Lie group with the finite number of identity elements and dimension , we show that every left invariant -form on is right invariant -form
UR - http://ijsts.shirazu.ac.ir/article_2079.html
L1 - http://ijsts.shirazu.ac.ir/article_2079_277b7a556e784b66d47e554b3a0f66b3.pdf
ER -