3 июн. 2015 г. · That S0, S1 and S3 are the only spheres with smooth group structure (i.e. Lie groups) can be deduced using Chevalley-Eilenberg's Lie algebra ...

21 мар. 2022 г. · Determine the Lie algebra of the unit-quaternions S3⊂H∗ and their left-invariant vector fields. Unfortunately I am struggling with quaternions.

17 мар. 2016 г. · Conversely, can Lie groups be converted into simplicial groups (in a more feasible way than applying the singular ss functor)? I was thinking ...

8 сент. 2014 г. · Isometries of S^3 and some Lie algebras ... By considering S3 as the group of unit quaternions, and letting it act on itself from both the left ...

5 нояб. 2018 г. · Show that a map f′:S3×S3→SO(4) induced from a map f:S3×S3→GL4(R) is a homomorphism where S3 is a Lie group of unit quaternion. Here, the map f ...

14 нояб. 2015 г. · The three-sphere, S3 is the group manifold for the Lie group SU(2). In terms of Lie algebra elements (i.e. left-invariant vector fields) ...

30 авг. 2021 г. · We know that the real 3-dimensional sphere is isomorphic and diffeomorphic to various Lie groups S3=Spin(3)=SU(2).

2 нояб. 2018 г. · Please help me,and give me more details! Thank you very much! differential-geometry · algebraic-topology · lie-groups.

28 мая 2018 г. · Consider the set S3⊂R4, as known S3 is a Lie Group and, therefore, is parallelizable. If we define the sets T1, T2 ...

7 дек. 2019 г. · The Lie group proof basically goes as follows: take the tangent space T at the identity, then left translation at g∈G maps it bijectively to the tangent space ...