On Wednesday, June 1, 2022 at 2:34:26 PM UTC+8 Nils Bruin wrote:
> On Wednesday, 1 June 2022 at 05:41:33 UTC+2 hongy...@gmail.com wrote: > >> On Wednesday, June 1, 2022 at 1:55:45 AM UTC+8 Nils Bruin wrote: >> >>> The "GO" mentioned here should correspond to the O(3;1) (or perhaps >>> O(1;3) ) mentioned in the wikipedia article. >>> >> >> Do you mean that these two ways of writing are a matter of convention? >> > > setting t,x,y,z as coordinates on 4-space, O(3;1) is the group of matrices > preserving the quadratic form t^2+x^2+y^2-z^2 (three plusses, one minus) > and O(1;3) the group of matrices preserving the quadratic form > t^2-x^2-y^2-z^2 (one plus, three minuses). > Hence, the definitions of the two groups are different: it's not just > convention. The two groups are isomorphic, though, and one isomorphism is > given by swapping t and z. > > Thank you for your explanation and clarification. Regards, HZ -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/661e7ba9-7207-4994-b069-191839b5978fn%40googlegroups.com.
