List questions from spin-geometry

137

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Can we get a Spin-like connection from a group reduction ${\rm GL}^+(4,\mathbb{R})/{\rm Spin}^c(3,1)$ or $\exp {\rm CL}(3,1)/{\rm Spin}^c(3,1)$?

Published on 26 Mar 2026 - 3:12

121

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Nice way to show that a covering space of a Lie group is also a Lie group?

Published on 24 Mar 2023 - 3:05

64

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Representation of spin group carrying a symplectic form

Published on 24 Mar 2023 - 16:41

66

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For every local section of a $SO(M)$ there exists precisely two local sections of $\text{Spin}(M)$

Published on 26 Mar 2026 - 3:12

37

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Lie algebra isomorphism $\mathfrak{spin}^+(t,s)\rightarrow so^+(t,s)$

Published on 15 Apr 2023 - 2:20

66

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What is the definition of $\mathrm{Hom}_{\mathrm{Cl}}(S,E)$?

Published on 15 Apr 2023 - 10:36

213

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Spinor representation of $SL_2(\mathbb{C})$ on Weyl Spinors.

Published on 19 Apr 2023 - 6:27

20

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Exponential of a spin connection belongs to what group?

Published on 21 Apr 2023 - 5:41

32

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Kernel for the Hodge chain homotopy

Published on 22 Mar 2026 - 15:04

53

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Definition of $\operatorname{Spin}^c(n)$ group

Published on 20 May 2023 - 20:59

93

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Clifford algebra $Cl_1 \cong \mathbb{C}$

Published on 26 Mar 2026 - 6:33

82

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Stiefel-Whitney classes in Čech cohomology

Published on 06 Jun 2023 - 16:47

105

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What's a double cover?

Published on 20 Jun 2023 - 15:29

55

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What's the explicit map building the double cover of SO(p,q)?

Published on 21 Jun 2023 - 7:42

41

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What is the representation that makes invariant Dirac equation?

Published on 27 Jun 2023 - 2:20

List Question

Can we get a Spin-like connection from a group reduction ${\rm GL}^+(4,\mathbb{R})/{\rm Spin}^c(3,1)$ or $\exp {\rm CL}(3,1)/{\rm Spin}^c(3,1)$?

Nice way to show that a covering space of a Lie group is also a Lie group?

Representation of spin group carrying a symplectic form

For every local section of a $SO(M)$ there exists precisely two local sections of $\text{Spin}(M)$

Lie algebra isomorphism $\mathfrak{spin}^+(t,s)\rightarrow so^+(t,s)$

What is the definition of $\mathrm{Hom}_{\mathrm{Cl}}(S,E)$?

Spinor representation of $SL_2(\mathbb{C})$ on Weyl Spinors.

Exponential of a spin connection belongs to what group?

Kernel for the Hodge chain homotopy

Definition of $\operatorname{Spin}^c(n)$ group

Clifford algebra $Cl_1 \cong \mathbb{C}$

Stiefel-Whitney classes in Čech cohomology

What's a double cover?

What's the explicit map building the double cover of SO(p,q)?

What is the representation that makes invariant Dirac equation?

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