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Reading @Qiaochu Yuan's blog the other day, I came across a new term: Poisson algebra. I had never heard of it before and wondered what other algebras are out there that I'm not aware of. Neither Wikipedia nor Google are of much help in this regard, since one can't regex google and Wikipedia has a rather paltry list of algebras.

Here are some algebras I'm familiar with:

  • Boolean algebra
  • Algebra of sets
  • various group algebras
  • Heyting algebra
  • Flag algebra
  • $\sigma$-algebras (OK, not really the same use of the word)
  • Exterior algebra

What are some more algebras that I'm missing out on?

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    [Term algebras](http://en.wikipedia.org/wiki/Term_algebra) in mathematical logic. Lots of special cases of associative algebras: offhand I can recall seeing Banach, Clifford, Hopf, incidence, and Lie algebras.2011-12-04
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    Here's a [WP list of algebras](http://en.wikipedia.org/wiki/List_of_algebraic_structures).2011-12-04
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    What is the purpose of constructing this list?2011-12-04
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    (I mean: I can probably name 50 «algebras»... What good would it be for the OP or anyone else?)2011-12-04
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    http://en.wikipedia.org/w/index.php?title=Special:Search&redirs=1&search=Algebra&limit=500&offset=02011-12-06
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    Such a list will never be complete - *Algebra* is a highly common word and I would guess there are new constructions each year that are named "Algebras".2011-12-08
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    It is higlhly context-dependent, ancient word, it can mean anything, from subject kids learning in school to special types of set with special operations and properties. So the list is useless.2013-07-12

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