Notation conventions

The following are symbols that are typically used to indicate specific types of variables in this book. These conventions will not always be possible to follow, but are as much as is practical.

 $${G,H;g,h}$$ Groups; elements of a group $${\phi}$$ Group homomorphism $${R;r}$$ Ring; element of a ring $${V,W;v,w;a,b}$$ Vector spaces; elements of a vector space; scalars in a vector space $${\hat{v}}$$ Unit length vector in a normed vector space $${\varphi,\psi}$$ Mappings or forms $${\vec{\varphi},\vec{\psi}}$$ Vector-valued forms (non-standard) $${\check{\Theta},\check{\Psi}}$$ Algebra-valued forms (non-standard) $${e_{\mu},\hat{e}_{\mu}}$$ Basis vectors or frame, orthonormal basis vectors or frame $${\beta^{\mu},\hat{\beta}^{\mu}}$$ Basis forms or dual frame, orthonormal basis forms or dual frame $${\mathfrak{a},\mathfrak{b}}$$ Algebras $${\mathfrak{g},\mathfrak{h}}$$ Lie algebras $${A,B}$$ Elements of a Lie or Clifford algebra $${T^{ab}{}_{c}}$$ Tensor using abstract index notation $${T^{\mu_{1}\mu_{2}}{}_{\nu_{1}}}$$ Tensor using component notation in a specific basis $${X,Y}$$ Topological spaces $${M,N}$$ Manifolds $${E,P,F}$$ Fiber bundle, principal bundle, abstract fiber