Below you will find example sentences with "spin group". The examples show how this phrase is used in natural context and which words often surround it.
Spin Group in a sentence
Corpus data
- Displayed example sentences: 11
- Discovered as a combination around: spin
- Corpus frequency in the collocation scan: 5
- Phrase length: 2 words
- Average sentence length: 25.9 words
Sentence profile
- Phrase position: 5 start, 6 middle, 0 end
- Sentence types: 11 statements, 0 questions, 0 exclamations
Corpus analysis
- The phrase "spin group" has 2 words and usually appears in the middle in these examples. The average sentence has 25.9 words and is mostly made up of statements.
- Around this phrase, patterns and context words such as of the spin group that does, 1 the spin group usually has, representation, spinors and space stand out.
- In the phrase index, this combination connects with group equities, lie group and advisory group, linking the page to nearby combinations.
Example types with spin group
This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:
The spin group is the group of rotations keeping track of the homotopy class. (14 words)
Formally, the spin group is the group of relative homotopy classes with fixed endpoints in the rotation group. (18 words)
Real spinors details To describe the real spin representations, one must know how the spin group sits inside its Clifford algebra. (21 words)
The space of spinors by definition is equipped with a (complex) linear representation of the spin group, meaning that elements of the spin group act as linear transformations on the space of spinors, in a way that genuinely depends on the homotopy class. (43 words)
More formally, the space of spinors can be defined as an ( irreducible ) representation of the spin group that does not factor through a representation of the rotation group (in general, the connected component of the identity of the orthogonal group ). (40 words)
Spin groups The spin representation is a vector space equipped with a representation of the spin group that does not factor through a representation of the (special) orthogonal group. (29 words)
Example sentences (11)
Spin groups The spin representation is a vector space equipped with a representation of the spin group that does not factor through a representation of the (special) orthogonal group.
The space of spinors by definition is equipped with a (complex) linear representation of the spin group, meaning that elements of the spin group act as linear transformations on the space of spinors, in a way that genuinely depends on the homotopy class.
Real spinors details To describe the real spin representations, one must know how the spin group sits inside its Clifford algebra.
The spin representation Δ further decomposes into a pair of irreducible complex representations of the Spin group Via the even-graded Clifford algebra.
Formally, the spin group is the group of relative homotopy classes with fixed endpoints in the rotation group.
More formally, the space of spinors can be defined as an ( irreducible ) representation of the spin group that does not factor through a representation of the rotation group (in general, the connected component of the identity of the orthogonal group ).
In this case, the spin group is isomorphic to the group of 2 2 unitary matrices with determinant one, which naturally sits inside the matrix algebra.
The spin group is the group of rotations keeping track of the homotopy class.
When the characteristic is not 2, these are the elements of determinant 1. The Spin group usually has index 2 in the Pin group.
As a representation of the spin group, this realization of spinors as (complex The metric signature relevant as well if we are concerned with real spinors.
The Spin group consists of those elements of Pin p, q which are products of an even number of unit vectors.