I'm really surprised that I can't seem to find a canonical means of representing a measurement like 1 meter in an algebra. I found George Hart's work from the 80s (Multidimensional analysis: algebras and systems for science and engineering), but it doesn't cover exactly what I expected.
I've found a recent preprint that puts forth a "Dimensioned Algebra" https://arxiv.org/pdf/2108.08703.pdf (2021), which uses a "semi-vector space" https://link.springer.com/article/10.1007/s10440-009-9505-6 (2009) but has it really taken till 2000s? Am I missing something fundamental? The preprint talks about a 100 year delay, but do people who care about Alegbras and people who care about measurements really not talk?
If I wanted to work with some sort of Algebra with units (doesn't have to be from the above authors), where would I look? I was hoping to maybe formalize some work I did in Lean, but I didn't realize there wasn't a settled representation.