The Unapologetic Mathematician

Mathematics for the interested outsider

Algebras

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May 8, 2007 - Posted by | Ring theory

11 Comments »

  1. […] one that we haven’t considered directly: let be a commutative ring with unit and let be an algebra over with unit. Then we have a homomorphism of rings sending to — the action of on the […]

    Pingback by Pushouts and pullbacks « The Unapologetic Mathematician | June 14, 2007 | Reply

  2. […] mention the Bracket polynomial and the Jones polynomial. Jones was studying a certain kind of algebra when he realized that the defining relations for these algebras were very much like those of the […]

    Pingback by What is Knot Homology? « The Unapologetic Mathematician | July 11, 2007 | Reply

  3. […] go any further into linear algebra. Specifically, we’ll need to know a few things about the algebra of polynomials. Specifically (and diverging from the polynomials discussed earlier) we’re […]

    Pingback by Polynomials I « The Unapologetic Mathematician | July 28, 2008 | Reply

  4. […] And, of course, once we’ve got monoids and -linearity floating around, we’re inexorably drawn — Serge would way we have an irresistable compulsion — to consider monoid objects in the category of -modules. That is: -algebras. […]

    Pingback by Algebra Representations « The Unapologetic Mathematician | October 24, 2008 | Reply

  5. […] or not. We know that the linear maps from a vector space (of finite dimension ) to itself form an algebra over . We can pick a basis and associate a matrix to each of these linear transformations. It turns […]

    Pingback by The Algebra of Upper-Triangular Matrices « The Unapologetic Mathematician | February 5, 2009 | Reply

  6. […] We’re about to talk about certain kinds of algebras that have the added structure of a “grading”. It’s not horribly important at the […]

    Pingback by Graded Objects « The Unapologetic Mathematician | October 23, 2009 | Reply

  7. […] and Symmetric Algebras There are a few graded algebras we can construct with our symmetric and antisymmetric tensors, and at least one of them will be […]

    Pingback by Tensor and Symmetric Algebras « The Unapologetic Mathematician | October 26, 2009 | Reply

  8. […] we proceed with the differential geometry: Lie algebras. These are like “regular” associative algebras in that we take a module (often a vector space) and define a bilinear operation on it. This much is […]

    Pingback by Lie Algebras « The Unapologetic Mathematician | May 17, 2011 | Reply

  9. […] Algebras from Associative Algebras There is a great source for generating many Lie algebras: associative algebras. Specifically, if we have an associative algebra we can build a lie algebra on the same […]

    Pingback by Lie Algebras from Associative Algebras « The Unapologetic Mathematician | May 18, 2011 | Reply

  10. […] called and give it a bilinear operation which we write as . We often require such operations to be associative, but this time we impose the following two […]

    Pingback by Lie Algebras Revisited « The Unapologetic Mathematician | August 6, 2012 | Reply

  11. […] off, we need an algebra over a field . This doesn’t have to be associative, as our algebras commonly are; all we […]

    Pingback by Derivations « The Unapologetic Mathematician | August 10, 2012 | Reply


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