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 Small research update MphLee Fellow Posts: 184 Threads: 19 Joined: May 2013 10/26/2021, 12:22 AM (This post was last modified: 10/26/2021, 01:26 AM by MphLee.) (10/25/2021, 08:40 PM)JmsNxn Wrote: I'm a little wary of the term Nixon-algebra; as I have no idea what it is and it has my name on it, LOL! The term Hilbert space comes with a funny anecdote on its origin: Saunders Mac Lane, one of the founding fathers of category theory, in [1989] writes Translation: "Dr. von Neumann, I would like to know what is a Hilbert space?" (tr. by $$n$$Lab) [1989] S. Mac Lane, 'Concepts and categories in perspective: Addendum', pp. 323–365 in A century of mathematics in America, part I. Edited by P. Duren, R. A. Askey, and U. C. Merzbach. History of Mathematics 1. American Mathematical Society (Providence, RI), 1988. An addendum to this article was published in History of Mathematics, part III (1989). ps: A $$\diamond$$-algebra/Nixon Algebra is something much bolder than what you are thinking then, yet,  originated from you. Let $$(J,{}^+)$$ be a set equipped with an function $${}^+:J\to J$$, i.e. a discrete dynamical system maaping $$\sigma \mapsto \sigma^+$$ that we call the system of ranks, define a Nixon algebra over $$J$$ - with ranks in $$J$$ - to be a pair $$(M,\diamond)$$ where $$M$$ is a monoid $$(M,\cdot, 1_M)$$; equipped with an operation $$\diamond:J\times M\to M$$ such that for every $$\sigma\in J$$ and $$f\in M$$ we have $$(\sigma^+\diamond f)\cdot f=(\sigma\diamond f)\cdot(\sigma^+\diamond f)$$ MathStackExchange account:MphLee Fundamental Law $(\sigma+1)0=\sigma (\sigma+1)$ « Next Oldest | Next Newest »

 Messages In This Thread Small research update - by MphLee - 10/24/2021, 11:57 AM RE: Small research update - by JmsNxn - 10/25/2021, 08:40 PM RE: Small research update - by MphLee - 10/26/2021, 12:22 AM

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