Hand and Bush
Jun. 15th, 2019 04:21 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowThe thing about group algebras that I talked about a while ago does, in fact, have implications for my research.
It ties together the two big pieces of machinery - the stuff that I started off with, which appears in Taxonomy I, and the newer stuff that I'm introducing in Taxonomy III. They're two manifestations of the same thing, and so *of course* they interact in interesting ways.
It also opens the door to an enormous generalization, to "G-gons", where G is a finite abelian group. Never mind what that means; the integers mod n form a finite abelian group, called Zn, and an n-sided polygon, under my Taxonomy I definition, is precisely a Zn-gon - but there are other possibilities!
This looks like it might be fascinating, but *I've got papers to write* - papers that I *know* contain interesting results. Bird in the hand...
I'm going to have to divide my time, this summer. The new stuff may be a will-o-wisp, but if not, it's *really neat*. Birds in the bush...
:moan:
It ties together the two big pieces of machinery - the stuff that I started off with, which appears in Taxonomy I, and the newer stuff that I'm introducing in Taxonomy III. They're two manifestations of the same thing, and so *of course* they interact in interesting ways.
It also opens the door to an enormous generalization, to "G-gons", where G is a finite abelian group. Never mind what that means; the integers mod n form a finite abelian group, called Zn, and an n-sided polygon, under my Taxonomy I definition, is precisely a Zn-gon - but there are other possibilities!
This looks like it might be fascinating, but *I've got papers to write* - papers that I *know* contain interesting results. Bird in the hand...
I'm going to have to divide my time, this summer. The new stuff may be a will-o-wisp, but if not, it's *really neat*. Birds in the bush...
:moan:
