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\title{LaTeX preambles} | ||
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\p{This tree defines} | ||
\p{Here we define:} | ||
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\ol{ | ||
\li{\code{\startverb\latex-preamble/common\stopverb}} | ||
} | ||
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\p{They are used by [[base-macros]].} | ||
\p{\code{latex-preamble/common}: Some common LaTeX preambles.} | ||
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\def\latex-preamble/common{ | ||
\startverb | ||
% because LaTeX is running in `build` directory | ||
\input{../trees/preamble} | ||
\stopverb | ||
} | ||
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\p{They are used by [[base-macros]].} |
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\title{Spin Geometry} | ||
\date{2019-03-05} | ||
\date{2024-04-26} | ||
\taxon{reference} | ||
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% \author{todo} | ||
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\title{Clifford algebra (Wikipedia)} | ||
\date{2019-03-05} | ||
\taxon{reference} | ||
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\p{See [Clifford algebra (Wikipedia)](https://en.wikipedia.org/wiki/Clifford_algebra).} |
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\title{Spin group ([[lawson2016spin]])} | ||
\date{2024-04-27} | ||
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\taxon{definition} | ||
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\import{base-macros} | ||
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\minitex{ | ||
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\texdef{Spin group}{lawson2016spin}{ | ||
The Pin group of $(V, q)$ is the subgroup $\operatorname{Pin}(V, q)$ of $P(V, q)$ generated by the elements $v \in V$ with $q(v) = \pm 1$. | ||
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The associated spin group of $(V, q)$ is then defined by | ||
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$$ | ||
\operatorname{Spin}(V, q)=\operatorname{Pin}(V, q) \cap \mathrm{Cl}^0(V, q) | ||
$$ | ||
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} |
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\title{Spin group (The wikipedia page on Clifford Algebras)} | ||
\date{2024-04-27} | ||
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\taxon{definition} | ||
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\import{base-macros} | ||
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\minitex{ | ||
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The pin group $\operatorname{Pin}_V(K)$ is the subgroup of the Lipschitz group $\Gamma$ of elements of spinor norm 1, and similarly the spin group $\operatorname{Spin}_V(K)$ is the subgroup of elements of Dickson invariant 0 in $\operatorname{Pin}_V(K)$. | ||
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} | ||
\texdef{Spin group}{wiki-0001}{ | ||
The pin group $\operatorname{Pin}_V(K)$ is the subgroup of the Lipschitz group $\Gamma$ of elements of spinor norm 1, and similarly the spin group $\operatorname{Spin}_V(K)$ is the subgroup of elements of Dickson invariant 0 in $\operatorname{Pin}_V(K)$. | ||
} |