Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
some minimum, for cross-linking with Sp(n).Sp(1)
When I started this entry, I deliberately changed the wording of the definition as compared to what one finds in most of the literature.
I have added now a remark on this point, for clarity:
Beware that most texts insists on stating the choices in the definition of the central product as that of
Beware that most texts insists on stating the choices in Def. \ref{CentralProduct} as that of
two separate subgroups $C_i \xhookrightarrow{\iota_i} Z(G_i)$
an isomorphism $C_1 \xrightarrow[\simeq]{\phi} C_2$ between them
and insists that the second group acts via $(-)^{-1}\circ \phi$.
These clauses matter if one thinks of the subgroup inclusions as in material set theory. But we speak structural set theory, which means that a subgroup inclusion as in (eq:SubgroupInclusion) is really a choice of monic homomorphism, and this choice already absorbs the choice of $\phi$ and or $(-)^{-1}\circ \phi$ above.
added mentioning of the example of spin^c-groups
1 to 4 of 4