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  • definition of $C^*$-subalgebra - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • abstract algebra - How to denote that something is a subalgebra . . .
    By far the most common way to denote this is to say "$\mathfrak{h}$ is a subalgebra of $\mathfrak{g}$" (or perhaps "$\mathfrak{h}\subseteq\mathfrak{g}$ is a subalgebra") There is not any common special notation for this
  • Question regarding the definition of ideal subalgebra of a Lie algebra . . .
    What is the relation between "derivations" and the "derived subalgebra" of a Lie algebra? 1 How can I show a the Cartan subalgebra being abelian implies its adjoint representation on the original Lie algebra completely commutes?
  • Must $k$-subalgebra of $k[x]$ be finitely generated?
    The very obvious question is whether there is a proof that does not use these fancy SAGBI bases I'll write again if I find an answer to that The important thing to know about them is, however, that a SAGBI basis for a subalgebra is a generating set with certain properties well-suited for computations
  • set theory - Complete Subalgebras and Dense Subalgebras of Complete . . .
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • Why is a semisimple Lie-subalgebra of - Mathematics Stack Exchange
    So a maximal rank subalgebra must have a Cartan subalgebra $\mathfrak{c}$ which is also a Cartan subalgebra of $\mathfrak{g}$ Note that this forces $\mathfrak{h}$ to be the span of $\mathfrak{c}$ together with some of the root spaces In fact these roots must form a subsystem of our original root system
  • lie algebras - How to find a Cartan subalgebra of $so (3 . . .
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • algebras - Subalgebra Definition - Mathematics Stack Exchange
    If A is an algebra over a field K, and B is a subalgebra, must B be an algebra over K or can it also be an algebra over some subfield of K? For example, if you take $\mathbb{R}$ as an algebra over $\mathbb{R}$, would it be correct to call $\mathbb{Q}$ a subalgebra, since it is an algebra over $\mathbb{Q}$?
  • subalgebras of a polynomial ring - Mathematics Stack Exchange
    One strategy which seems to work okay in practice (e g to compute generators of subalgebras invariant under a group action) is to somehow compute the Hilbert series of the subalgebra you care about and then identify enough generators that you can show the subalgebra spanned by the generators has the same Hilbert series as the whole thing





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