Rename base-macros

templates/texdef.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{}{
 

trees/latex-preamble.tree

@@ -11,4 +11,4 @@
  \stopverb
 }
 
-\p{They are used by [[base-macros]].}
+\p{They are used by [[macros]].}

trees/refs/nlab-spin.tree

@@ -1,3 +1,3 @@
-\import{base-macros}
+\import{macros}
 
 \nlabref{Spin group}{spin+group}

trees/refs/wiki-clifford.tree

@@ -1,3 +1,3 @@
-\import{base-macros}
+\import{macros}
 
 \wikiref{Clifford algebra}{Clifford_algebra}

trees/refs/wiki-spin.tree

@@ -1,3 +1,3 @@
-\import{base-macros}
+\import{macros}
 
 \wikiref{Spin group}{Spin_group}

trees/spin-0001.tree

@@ -2,7 +2,7 @@
 
 \taxon{Article}
 
-\import{base-macros}
+\import{macros}
 
 \meta{venue}{Clifford Algebra}
 \meta{source}{ \edit{spin-0001} }

trees/spin-0002.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{lawson2016spin}{
 

trees/spin-0003.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{wiki-clifford}{
     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 $\operatorname{Pin}_V(K)$.

trees/spin-0004.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{li2008invariant}{
 A versor refers to a Clifford monomial composed of invertible vectors. It is called a rotor, or spinor, if the number of vectors is even. It is called a unit versor if its magnitude is 1.

trees/spin-0005.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{sommer2013geometric}{
 

trees/spin-0006.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{perwass2009geometric}{
 A versor is a multivector that can be expressed as the geometric product of a number of non-null 1-vectors. That is, a versor $\boldsymbol{V}$ can be written as $\boldsymbol{V}=\prod_{i=1}^k \boldsymbol{n}_i$, where $\left\{\boldsymbol{n}_1, \ldots, \boldsymbol{n}_k\right\} \subset \mathbb{G}_{p, q}^{\varnothing 1}$ with $k \in \mathbb{N}^{+}$, is a set of not necessarily linearly independent vectors.

trees/spin-0007.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{jadczyk2019notes}{
 

trees/spin-0008.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{garling2011clifford}{
 Suppose that $(E, q)$ is a regular quadratic space. We consider the action of $\mathcal{G}(E, q)$ on $\mathcal{A}(E, q)$ by adjoint conjugation. We set

trees/spin-0009.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{meinrenken2009lie}{
 Recall that $\Pi: \mathrm{Cl}(V) \rightarrow$ $\mathrm{Cl}(V), x \mapsto(-1)^{|x|} x$ denotes the parity automorphism of the Clifford algebra. Let $\mathrm{Cl}(V)^{\times}$be the group of invertible elements in $\mathrm{Cl}(V)$.

trees/spin-000A.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{weber2013lie}{
 The ``group of units" in $C l_{p, q}$, denoted $C l_{p, q}^{\times}$, is the group of all invertible elements. 

trees/spin-000B.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{bar2011spin}{
 We define the Pin $\operatorname{group} \operatorname{Pin}(\boldsymbol{n})$ by

trees/spin-000C.tree

@@ -1,5 +1,5 @@
 \date{2024-04-29}
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{woit2012lie}{
 There are several equivalent possible ways to go about defining the $\operatorname{Spin}(n)$ groups as groups of invertible elements in the Clifford algebra.

trees/spin-000D.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{liu2016lie}{
 The space of quadratic vectors in $\mathrm{Cl}$ is the Lie algebra of $\mathrm{SO}(n)$. The corresponding Lie group, called the Spin group $\operatorname{Spin}(Q)$, is the set of invertible elements $x \in \mathrm{Cl}$ that preserve $V$ under $v \mapsto x v x^{-1}$. Clearly this map is in $\mathrm{SO}(V, Q)$ since it preserves the quadratic form $Q$, and is a two-fold cover with kernel $\pm 1$.

trees/spin-000E.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{figueroa2010spin}{
 The Pin group Pin $(V)$ of $(V, Q)$ is the subgroup of (the group of units of) $C \ell(V)$ generated by $v \in \mathrm{V}$ with $\mathrm{Q}(v)= \pm 1$. In other words, every element of $\operatorname{Pin}(\mathrm{V})$ is of the form $u_1 \cdots u_r$ where $u_i \in \mathrm{V}$ and $\mathrm{Q}\left(u_i\right)= \pm 1$. We will write $\operatorname{Pin}(s, t)$ for $\operatorname{Pin}\left(\mathbb{R}^{s, t}\right)$ and $\operatorname{Pin}(n)$ for $\operatorname{Pin}(n, 0)$.

trees/spin-000F.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{lundholm2009clifford}{
 We identify the following groups embedded in $\mathcal{G}$ :

trees/spin-000G.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{renaud2020clifford}{
 The Clifford group $\Gamma(p, q)$ is the (multiplicative) group generated by invertible 1-vectors in $R^{p, q}$.

trees/spin-000H.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{dutailly2018clifford}{
 The Spin group $\operatorname{Spin}(F, \rho)$ of $C l(F, \rho)$ is the subset of $C l(F, \rho)$ whose elements can be written as the product $g=u_1 \cdot \ldots \cdot u_{2 p}$ of an even number of vectors of $F$ of norm $\left\langle u_k, u_k\right\rangle=1$.

trees/spin-000I.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{hitzer2012introduction}{
 

trees/spin-000J.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{hahn2004clifford}{
 We continue to let $F$ be a field of characteristic not 2 and $M$ a quadratic space over $F$.

trees/spin-000K.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{porteous1995clifford}{
 Let $g$ be an invertible element of a universal Clifford algebra $A$ such that, for each $x \in X, g x \widehat{g}^{-1} \in X$. Then the map

trees/spin-000L.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{rosen2019geometric}{
 Let $V$ be an inner product space. We denote by $\Delta V$ the standard Clifford algebra $(\wedge V,+, \Delta)$ defined by the Clifford product $\Delta$ on the space of multivectors in $V$.

trees/spin-000M.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{ruhe2024clifford}{
 

trees/spin-000N.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{gallier2014clifford}{
 

trees/spin-000O.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{fulton2013representation}{
 Instead of defining the spin group as the set of products of certain elements of $V$, it will be convenient to start with a more abstract definition. Set

trees/spin-000P.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{wiki-spin}{
 The pin group $\operatorname{Pin}(V)$ is a subgroup of $\mathrm{Cl}(V)$ 's Clifford group of all elements of the form

trees/spin-000Q.tree

@@ -1,4 +1,4 @@
-\import{base-macros}
+\import{macros}
 
 \texdef{Spin group}{nlab-spin}{
 The Pin group $\operatorname{Pin}(V ; q)$ of a quadratic vector space, is the subgroup of the group of units in the Clifford algebra $\mathrm{Cl}(V, q)$

trees/uts-0001.tree

@@ -4,7 +4,7 @@
 
 \date{2024-04-24}
 
-\import{base-macros}
+\import{macros}
 
 \p{[Experimenting](uts-0002), see the following for some math:}
 

trees/uts-0002.tree

@@ -16,4 +16,4 @@
 
 \p{To find the source of a page including the LaTeX, head over [my forest repository](https://github.com/utensil/forest) and use "Go to file" to search for the "note ID" that looks like e.g. "spin-0001".}
 
-\p{To find macros used in the forest, check out [[base-macros]].}
+\p{To find macros used in the forest, check out [[macros]].}