𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the Surjectivity of the Exponential Function of Complex Algebraic, Complex Semisimple, and Complex Splittable Lie Groups

✍ Scribed by Michael Wüstner

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
166 KB
Volume
184
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

The surjectivity of the exponential function of complex algebraic, in particular of complex semisimple Lie groups, and of complex splittable Lie groups is equivalent to the connectedness of the centralizers of the nilpotent elements in the Lie algebra. This implies that the only complex semisimple Lie groups with surjective exponential function are isomorphic to finite products of the adjoint groups of Ž . SL n, ‫ރ‬ .

📜 SIMILAR VOLUMES

Historical Remarks on the Surjectivity o
Historical Remarks on the Surjectivity of the Exponential Function of Lie Groups
✍ Michael Wüstner 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 82 KB

In 1892, F. Engel and E. Study investigated the exponential map of classical Lie groups for the first time. They showed that the special projective Lie groups over C possess surjective exponential functions. Engel also gave a "proof" for the corresponding claims for the other projective classical gr

Steinness of the Total Space of a Non-Tr
Steinness of the Total Space of a Non-Trivial Algebraic Affine ℂ-Bundle on the Punctured Complex Affine Plane
✍ Makoto Abe 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB

We prove that the total space E of an algebraic affine C -bundle π : E → X on the punctured complex affine plane X := C 2 -{(0, 0)} is Stein if and only if it is not isomorphic to the trivial holomorphic line bundle X × C . ## 0. Introduction Let π : E → X be a holomorphic affine C -bundle on the

The effect of training data set size and
The effect of training data set size and the complexity of the separation function on neural network classification capability: The two-group case
✍ Moshe Leshno; Yishay Spector 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 136 KB 👁 3 views

Classification among groups is a crucial problem in managerial decision making. Classification techniques are used in: identifying stressed firms, classifying among consumer types, and rating of firms' bonds, etc. Neural networks are recognized as important and emerging methodologies in the area of