Classification of real three-dimensional Poisson–Lie groups
نویسندگان
چکیده
منابع مشابه
On Three-Dimensional Space Groups
A entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 “irreducible” groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short “fibrifold name...
متن کاملInfinite-dimensional Representations of Real Reductive Groups
is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...
متن کاملClassification, Automorphism Groups and Categorical Structure of the Two-Dimensional Real Division Algebras
The category of all 2-dimensional real division algebras is shown to split into four full subcategories each of which is given by the natural action of a Coxeter group of type A1 or A2 on the set of all pairs of ellipses in R which are centred in the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are being determined. They yield a classificatio...
متن کاملFeedback Classification of Invariant Control Systems on Three-Dimensional Lie Groups
We consider left-invariant control affine systems evolving on Lie groups. In this context, feedback equivalence specializes to detached feedback equivalence. We characterize (local) detached feedback equivalence in a simple algebraic manner. We then classify all (full-rank) systems evolving on three-dimensional Lie groups. A representative is identified for each equivalence class. Systems on th...
متن کاملThree-dimensional classification of thoracic scoliotic curves.
STUDY DESIGN Three-dimensional (3D) characterization of the thoracic scoliotic spine (cross-sectional study). OBJECTIVES To investigate the presence of subgroups within Lenke type-1 curves by evaluating the thoracic segment indices extracted from 3D reconstructions of the spine, and to propose a new clinically relevant means (the daVinci representation) to report 3D spinal deformities. SUMM...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/17/175204