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nLab > Latest Changes

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    • nonassociative groups: loops whose left and right inverses are the same

      Anonymous

      v1, current

    • Created Moufang loop and some links. It would be good to update the proof that the tangent bundle of a Lie group is trivial to include the case of the tangent bundle of a smooth Moufang loop.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

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      Anonymous

      v1, current

    • quasigroups that are associative

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Added how small categories can be thought of as semigroups.

      Adam

      diff, v22, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Added comment about one-sided units, and the fact units in a magma may fail to be unique.

      diff, v11, current

    • I have added to alternative algebra the characterization in terms of skew-symmetry of the associator.

    • just for completeness and for ease of hyperlinking

      v1, current

    • Added the definition of “basic triples” of octonions, and the statement that they form a torsor over Aut(𝕆)=G2.

    • I am giving this its own page, in order to have a way to point to quaternionic conjugation etc.

      (Previously “complex conjugation” just redirected to “complex number”.)

      v1, current

    • made explicit the alternative form of the definition (here) in terms of adjoining a generator and imposing relations

      diff, v17, current

    • PhD-thesis on categorical aspects of vN-algebras. We’ll probably want to include more results from it.

      diff, v50, current

    • I have made explicit the example of involutive Hopf algebras, and how most of the other examples previously listed here are special cases of this one. Also expanded a little and organized it all into a new Examples-subsection (here)

      diff, v14, current

    • a stub, for the moment just to satisfy some links

      v1, current

    • an algebra with a two-sided inverse for all non-zero elements

      Anonymous

      v1, current

    • stub right now, I hope to write about some of the smooth and analytic properties of real-valued cubic functions and their inverses in the same way I did for real quadratic functions

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

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      Anonymous

      v1, current

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      Anonymous

      v1, current

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      Anonymous

      v1, current

    • starting article on a degree of a polynomial, since its entry in the disambiguation page degree linked to a nonexistent page.

      Anonymous

      v1, current

    • I wrote out a proof which uses very little machinery at fundamental theorem of algebra. It is just about at the point where it is not only short and rigorous, but could be understood by an eighteenth-century mathematician. (Nothing important, just fun!)

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • at normed division algebra it used to say that “A normed field is either ℝ or ℂ. ” I have changed that to “a normed field over ℝ is…” and changed normed field from being a redirect to “normed division algebra” to instead being an entry on its own.

    • Rewriting to prioritize a more standard definition of “division algebra,” while preserving the material and citation to Baez’s less standard version.

      diff, v10, current

    • I am trying to imrpove the complex of entries revolving around the Hurwitz theorem. I am not done yet at all, but since in the process I am touching a lot of entries, I thought I’d drop a note now for those anxiously following the RecentlyRevised notifications.

      So I gave Hurwitz theorem its own entry, first of all, cross linking to the details (a proof,in fact), that may be found at composition algebra, but which previously could not be found from normed division alegbra. Now there are cross-links.

      I also tried to add more references, but this needs work. It seems that Wikipedia says both that the source is

      • Adolf Hurwitz, Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Ges. Wiss. Göttingen (1898) 309–316

      as well as that “was published posthumously in 1923”.

      But I haven’t really spent much effort yet to check.

      I also added cross-links with Hopf invariant one, but this is plain stubby for the moment.

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • adding disambiguation message at top of page for the term “monic”

      Anonymous

      diff, v3, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

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